Finite Mathematics Quiz: Break Even And Cost Revenue Analysis
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Break Even And Cost Revenue AnalysisQuestion 1 of 15

Two competing pizza shops have the following cost structures: Shop A has fixed costs of $2,400 per month with variable costs of $3 per pizza, while Shop B has fixed costs of $1,800 per month with variable costs of $4 per pizza. Both shops sell pizzas for $12 each. At what monthly sales volume will both shops have identical total profits?

600 pizzas per month for both shops combined
600 pizzas per month for each shop individually
800 pizzas per month for each shop individually
1,200 pizzas per month for each shop individually
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Finite Mathematics Quiz

Finite Mathematics Quiz: Break Even And Cost Revenue Analysis

Practice Break Even And Cost Revenue Analysis in Finite Mathematics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Break Even And Cost Revenue Analysis, giving you a quick way to practice the rules, question types, and explanations that matter most for Finite Mathematics.

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Question 1

Two competing pizza shops have the following cost structures: Shop A has fixed costs of $2,400 per month with variable costs of $3 per pizza, while Shop B has fixed costs of $1,800 per month with variable costs of $4 per pizza. Both shops sell pizzas for $12 each. At what monthly sales volume will both shops have identical total profits?

  1. 600 pizzas per month for both shops combined
  2. 600 pizzas per month for each shop individually (correct answer)
  3. 800 pizzas per month for each shop individually
  4. 1,200 pizzas per month for each shop individually
Explanation: Shop A profit: $12x - $3x - $2,400 = $9x - $2,400. Shop B profit: $12x - $4x - $1,800 = $8x - $1,800. Setting equal: $9x - $2,400 = $8x - $1,800, so x = 600 pizzas per shop. Choice A incorrectly assumes combined volume, while C and D result from computational errors.

Question 2

Two companies are considering a merger. Company A has monthly fixed costs of $50,000 and variable costs of $15 per unit, while Company B has monthly fixed costs of $30,000 and variable costs of $20 per unit. Both sell identical products for $35 per unit. After the merger, fixed costs would be $65,000 monthly (due to elimination of duplicate overhead), and variable costs would be $17 per unit (average of both companies). If both companies currently sell the same number of units individually, at what total monthly sales volume would the merged company achieve the same total profit as both companies operating separately?

  1. 4,167 units per month for the merged company
  2. 4,444 units per month for the merged company
  3. 5,000 units per month for the merged company
  4. 5,556 units per month for the merged company (correct answer)
Explanation: Let x = units sold by each company separately, so total separate volume is 2x. Company A profit: (35-15)x - 50,000 = 20x - 50,000. Company B profit: (35-20)x - 30,000 = 15x - 30,000. Combined separate profit: 35x - 80,000. For the merged company selling volume y: (35-17)y - 65,000 = 18y - 65,000. Setting merged profit equal to combined separate profit at equal total volume (y = 2x): 18y - 65,000 = 35(y/2) - 80,000. Solving: 18y - 65,000 = 17.5y - 80,000, so 0.5y = -15,000, giving y = 5,556 units.

Question 3

A software company sells a subscription for $50 per month. The variable cost associated with each user is $10 per month, and the total monthly fixed costs are $80,000. The company is currently operating at a monthly profit of $40,000. Management is considering a new advertising campaign that will increase fixed costs by 20%. To justify this expense, the campaign must increase the company's monthly profit by 10%. What is the minimum number of additional monthly subscriptions the company must sell to achieve this goal?

  1. 100
  2. 400
  3. 500 (correct answer)
  4. 3,500
Explanation: First, determine the current number of subscriptions sold. The profit function is P(x)=R(x)−C(x)P(x) = R(x) - C(x). The contribution margin per unit is Price - Variable Cost = $50 - $10 = $40. So, $P(x) = 40x - 80000.Giventhecurrentprofitis$40,000,wecansolvefor$x. Given the current profit is $40,000, we can solve for $x: 40000=40x−80000⇒120000=40x⇒x=300040000 = 40x - 80000 \Rightarrow 120000 = 40x \Rightarrow x = 3000 subscriptions. Next, determine the new fixed costs and target profit. New fixed costs are $80000 \times 1.20 = $96,000. New target profit is $40000 \times 1.10 = 44,000.Now,findthenumberofsubscriptions(44,000. Now, find the number of subscriptions (x')neededtomeetthenewtarget:) needed to meet the new target: 44000 = 40x' - 96000 \Rightarrow 140000 = 40x' \Rightarrow x' = 3500subscriptions.Thequestionasksfortheadditionalsubscriptionsneeded,whichissubscriptions. The question asks for the additional subscriptions needed, which is3500 - 3000 = 500$.

Question 4

A manufacturing firm is choosing between two production technologies for a new product that will sell for $70 per unit. Technology A has fixed costs of $150,000 and a variable cost of $25 per unit. Technology B has fixed costs of $90,000 and a variable cost of $40 per unit. At what minimum sales volume does the profit from Technology A first exceed the profit from Technology B?

  1. 3,000 units
  2. 3,334 units
  3. 4,000 units
  4. 4,001 units (correct answer)
Explanation: Let xx be the number of units sold. The profit function for Technology A is PA(x)=(70−25)x−150000=45x−150000P_A(x) = (70 - 25)x - 150000 = 45x - 150000. The profit function for Technology B is PB(x)=(70−40)x−90000=30x−90000P_B(x) = (70 - 40)x - 90000 = 30x - 90000. To find where the profit from A exceeds the profit from B, we set up the inequality PA(x)>PB(x)P_A(x) > P_B(x): 45x−150000>30x−9000045x - 150000 > 30x - 90000. Subtracting 30x30x from both sides gives 15x−150000>−9000015x - 150000 > -90000. Adding 150,000150,000 to both sides gives 15x>6000015x > 60000. Dividing by 15 gives x>4000x > 4000. The smallest integer number of units greater than 4,000 is 4,001.

Question 5

A company achieves its break-even point when it sells 5,000 units per month. The company's fixed costs are $200,000 per month. If the company sells 5,800 units in a given month, what is its profit for that month?

  1. $32,000 (correct answer)
  2. $40,000
  3. $200,000
  4. $232,000
Explanation: The break-even point formula is x=F/(p−v)x = F / (p - v), where FF is fixed costs and (p−v)(p - v) is the contribution margin per unit. We are given x=5,000x=5,000 and F=$200,000.Wecanfindthecontributionmargin:$5000=200000/(p−v)⇒(p−v)=200000/5000=$40.Profitisonlygeneratedonunitssoldabovethebreak−evenpoint.Thenumberofprofit−generatingunitsisF=$200,000. We can find the contribution margin: $5000 = 200000 / (p - v) \Rightarrow (p - v) = 200000 / 5000 = $40. Profit is only generated on units sold above the break-even point. The number of profit-generating units is 5800 - 5000 = 800.Thetotalprofitisthenumberofextraunitsmultipliedbythecontributionmarginperunit:. The total profit is the number of extra units multiplied by the contribution margin per unit: Profit = 800 \times $40 = 32,00032,000.

Question 6

A company's cost function is C(x)=50x+10000C(x) = 50x + 10000 and its revenue function is R(x)=75xR(x) = 75x. Management implements changes that increase fixed costs by 10% and decrease the variable cost per unit by $5. How does the break-even quantity change?

  1. It decreases by 67 units.
  2. It decreases by 33 units. (correct answer)
  3. It increases by 33 units.
  4. It increases by 40 units.
Explanation: First, calculate the original break-even point by setting R(x)=C(x)R(x) = C(x): 75x=50x+10000⇒25x=10000⇒xold=40075x = 50x + 10000 \Rightarrow 25x = 10000 \Rightarrow x_{old} = 400 units. Next, determine the new cost function parameters. The new fixed cost is $10000 \times 1.10 = $11,000. The new variable cost per unit is $50 - 5 = $45. The new cost function is $C'(x) = 45x + 11000.Now,calculatethenewbreak−evenpoint:. Now, calculate the new break-even point: 75x = 45x + 11000 \Rightarrow 30x = 11000 \Rightarrow x_{new} = 11000 / 30 \approx 366.67units.Thechangeisunits. The change isx_{new} - x_{old} = 366.67 - 400 = -33.33$. The break-even quantity decreases by approximately 33 units.

Question 7

A company sells a product for $120. The variable cost per unit is 60% of the selling price. The company's fixed costs are $96,000. The company projects a loss of $12,000 for the upcoming period. How many additional units must be sold to transform this projected loss into a target profit of $24,000?

  1. 500
  2. 750 (correct answer)
  3. 1,750
  4. 2,500
Explanation: First, determine the contribution margin per unit. The variable cost is v=0.60×$120=$72.Thecontributionmarginis$p−v=$120−$72=$48.Thetotalchangeinprofitrequiredisfromalossof$12,000toaprofitof$24,000,whichisatotalswingofv = 0.60 \times $120 = $72. The contribution margin is $p - v = $120 - $72 = $48. The total change in profit required is from a loss of $12,000 to a profit of $24,000, which is a total swing of 24,000 - (-$12,000) = $36,000. Each additional unit sold contributes $48 to covering fixed costs and generating profit. To find the number of additional units needed, divide the required profit change by the contribution margin per unit: Additional Units = $36,000 / $48 = 750 units.

Question 8

A firm's break-even quantity is determined by its fixed costs FF, its selling price per unit pp, and its variable cost per unit vv, where p>vp>v. If both the selling price pp and the variable cost vv increase by the same positive dollar amount, kk, what is the effect on the break-even quantity?

  1. The break-even quantity increases.
  2. The break-even quantity decreases.
  3. The break-even quantity remains unchanged. (correct answer)
  4. The effect cannot be determined without knowing the values of F,p,F, p, and vv.
Explanation: The formula for the break-even quantity is xBE=F/(p−v)x_{BE} = F / (p - v). The term (p−v)(p - v) is the contribution margin. The new price is p′=p+kp' = p + k, and the new variable cost is v′=v+kv' = v + k. The new contribution margin is (p′−v′)=(p+k)−(v+k)=p−v(p' - v') = (p + k) - (v + k) = p - v. Since the fixed costs FF are unchanged and the contribution margin (p−v)(p - v) is also unchanged, the new break-even quantity, xBE′=F/(p′−v′)x'_{BE} = F / (p' - v'), is identical to the original break-even quantity.

Question 9

A company has a linear cost function and a linear revenue function. At a production level of 1,000 units, the total cost is $80,000 and the profit is $10,000. At a production level of 1,500 units, the total cost is $110,000. What is the company's fixed cost?

  1. $10,000
  2. $20,000 (correct answer)
  3. $30,000
  4. $60,000
Explanation: The cost function is linear, C(x)=vx+FC(x) = vx + F. We have two points on the cost function: (1000, 80000) and (1500, 110000). The variable cost per unit, vv, is the slope of the cost function: v=(110000−80000)/(1500−1000)=30000/500=$60.Nowwecanuseoneofthepointstofindthefixedcost,$Fv = (110000 - 80000) / (1500 - 1000) = 30000 / 500 = $60. Now we can use one of the points to find the fixed cost, $F. Using the first point: C(1000)=60(1000)+F=80000C(1000) = 60(1000) + F = 80000. This simplifies to 60000+F=8000060000 + F = 80000, so $F = $20,000. The information about profit is consistent but not needed to find the fixed cost.

Question 10

A company produces two products, Alpha and Beta. Product Alpha has a contribution margin of $10 per unit and Product Beta has a contribution margin of $15 per unit. The company's sales data shows a consistent sales mix of 3 units of Alpha for every 2 units of Beta. If the total fixed costs for the company are $240,000, how many units of Product Beta are sold at the break-even point?

  1. 4,000
  2. 7,680
  3. 8,000 (correct answer)
  4. 12,000
Explanation: To solve a multi-product break-even problem, create a 'bundle' based on the sales mix. One bundle consists of 3 units of Alpha and 2 units of Beta. Calculate the contribution margin of one bundle: CMbundle=(3×CMAlpha)+(2×CMBeta)=(3×$10)+(2×$15)=$30+$30=$60.Next,findthenumberofbundlesneededtobreakeven:Bundlestobreakeven=TotalFixedCosts/$CMbundle=$240,000/$60=4,000bundles.ThequestionasksforthenumberofunitsofProductBeta.Sinceeachbundlecontains2unitsofBeta,thetotalnumberofBetaunitsisCM_{bundle} = (3 \times CM_{Alpha}) + (2 \times CM_{Beta}) = (3 \times $10) + (2 \times $15) = $30 + $30 = $60. Next, find the number of bundles needed to break even: Bundles to break even = Total Fixed Costs / $CM_{bundle} = $240,000 / $60 = 4,000 bundles. The question asks for the number of units of Product Beta. Since each bundle contains 2 units of Beta, the total number of Beta units is 4,000 \text{ bundles} \times 2 \text{ units/bundle} = 8,000$ units.

Question 11

A company has a revenue function R(x)=150xR(x) = 150x and a cost function C(x)=90x+48000C(x) = 90x + 48000. Management is considering a price reduction of 10% to boost sales. They estimate that this will increase the number of units sold by 25%. If the company is currently operating exactly at its break-even point, what will be the net effect on profit from implementing these changes?

  1. An increase in profit of $12,000
  2. An increase in profit of $3,000
  3. No change in profit
  4. A decrease in profit of $3,000 (correct answer)
Explanation: First, find the current break-even point: 150x=90x+48000⇒60x=48000⇒x=800150x = 90x + 48000 \Rightarrow 60x = 48000 \Rightarrow x = 800 units. At this point, the current profit is $0. Next, evaluate the proposed changes. The new price is $p' = 150 \times (1 - 0.10) = $135. The new sales volume is $x' = 800 \times (1 + 0.25) = 1000units.Thecostfunctionparameters( units. The cost function parameters (v=90, F=48000)areunchanged.Calculatethenewprofit:) are unchanged. Calculate the new profit: P' = R'(x') - C(x') = (135 ×\times 1000) - (90 ×\times 1000 + 48000) = 135000 - (90000 + 48000) = 135000 - 138000 = -3,000.Theneteffectisthenewprofitminustheoldprofit,whichis−3,000. The net effect is the new profit minus the old profit, which is -3,000 - 0=−0 = -3,000. This is a decrease in profit of $3,000.

Question 12

A company manufactures an item with a variable cost of $80 per unit and fixed costs of $300,000. The company aims for a target profit of 150,000byselling5,000units.Duetoasupplychainissue,thevariablecostperunitisprojectedtoincreaseby15150,000 by selling 5,000 units. Due to a supply chain issue, the variable cost per unit is projected to increase by 15%. To maintain the same target profit (150,000) at the same sales volume (5,000 units), by what amount must the selling price per unit be increased?

  1. $12.00 (correct answer)
  2. $13.50
  3. $22.50
  4. $25.50
Explanation: The increase in variable cost per unit is $80 \times 0.15 = $12. For the profit to remain unchanged at a constant sales volume, the total revenue must increase by the same amount as the total cost. The total cost increases by (increase in variable cost per unit) $\times(numberofunits),whichis$12×5000=$60,000.Theincreaseintotalrevenueis(increaseinpriceperunit)$× (number of units), which is $12 \times 5000 = $60,000. The increase in total revenue is (increase in price per unit) $\times (number of units). Let Δp\Delta p be the price increase. Then Δp×5000=$60,000.Solvingfor$Δp\Delta p \times 5000 = $60,000. Solving for $\Delta p gives $\Delta p = $60,000 / 5000 = $12. Therefore, the price must be increased by $12.00.

Question 13

A concert promoter has fixed costs of $180,000 for a venue. The variable cost per attendee is $25. The ticket price is set at $75. A new city ordinance imposes a tax of 10% on the ticket price, which the promoter must pay from the proceeds of each ticket. How does the imposition of this tax affect the number of tickets that must be sold to break even?

  1. It increases by 360 tickets.
  2. It increases by 400 tickets.
  3. It increases by approximately 636 tickets. (correct answer)
  4. It increases to a total of 4,000 tickets.
Explanation: First, calculate the original break-even point. The contribution margin is CM=$75−$25=$50.Theoriginalbreak−evenpointis$xBE=F/CM=180000/50=3600CM = $75 - $25 = $50. The original break-even point is $x_{BE} = F / CM = 180000 / 50 = 3600 tickets. Next, calculate the effect of the tax. The tax is 10% of the $75 ticket price, which is $0.10 \times 75 = $7.50. This tax reduces the revenue per ticket, so the new effective contribution margin is $CM' = ($75 - $7.50) - $25 = $67.50 - $25 = $42.50. The new break-even point is $x'_{BE} = 180000 / 42.50 \approx 4235.29,whichmeans4,236ticketsmustbesold.Thechangeis, which means 4,236 tickets must be sold. The change is 4236 - 3600 = 636$ tickets.

Question 14

A company's monthly cost function is C(x)=8000+25x+0.02x2C(x) = 8000 + 25x + 0.02x^2 and revenue function is R(x)=75x−0.01x2R(x) = 75x - 0.01x^2, where xx is the number of units produced and sold. The company is considering a process improvement that would reduce the coefficient of x2x^2 in the cost function from 0.02 to 0.015, but would increase fixed costs to $9,200. At what production level would the profit improvement from this change be exactly $500?

  1. 1,000 units with profit improvement of exactly $500
  2. 1,200 units with profit improvement of exactly $500
  3. 1,414 units with profit improvement of exactly $500 (correct answer)
  4. 1,600 units with profit improvement of exactly $500
Explanation: Original profit: P₁(x) = 75x - 0.01x² - 8000 - 25x - 0.02x² = 50x - 0.03x² - 8000. New profit: P₂(x) = 75x - 0.01x² - 9200 - 25x - 0.015x² = 50x - 0.025x² - 9200. Improvement: P₂(x) - P₁(x) = -0.025x² + 0.03x² - 9200 + 8000 = 0.005x² - 1200. Setting equal to 500: 0.005x² - 1200 = 500, so 0.005x² = 1700, thus x² = 340,000, and x = 1,414 units. Other choices result from computational errors in the quadratic terms.

Question 15

A manufacturing company produces widgets with fixed costs of $15,000 monthly and variable costs of $6 per widget. The selling price follows the demand equation $p=30−0.001qp = 30 - 0.001q ,where, where pp ispriceindollarsandis price in dollars and qq $ is quantity. What quantity should be produced to maximize monthly profit?

  1. 12,000 widgets with maximum profit of $129,000 (correct answer)
  2. 12,000 widgets with maximum profit of $144,000
  3. 15,000 widgets with maximum profit of $144,000
  4. 18,000 widgets with maximum profit of $129,000
Explanation: Revenue = q(30 - 0.001q) = 30q - 0.001q². Profit = 30q - 0.001q² - 6q - 15,000 = 24q - 0.001q² - 15,000. Taking derivative: 24 - 0.002q = 0, so q = 12,000. Maximum profit = 24(12,000) - 0.001(12,000)² - 15,000 = 288,000 - 144,000 - 15,000 = $129,000. Choice B uses incorrect profit calculation, C and D have wrong quantities.