Finite Mathematics Quiz: Choosing Methods

A marketing research firm has collected data on customer demographics, purchase history, and satisfaction ratings for 500 customers across three different product categories. The firm wants to predict which customers are most likely to respond positively to a new product launch campaign, and they have historical data showing response rates for similar campaigns based on various customer characteristics.

What mathematical approach would be most effective for developing a predictive model to identify high-probability responders?

A transportation company operates a network connecting 6 cities. The company has data on travel times, fuel costs, and demand between each pair of cities. Due to new regulations, the company must restructure its routes to minimize total operating costs while ensuring that each city is connected to the network and that no route exceeds 8 hours of travel time.

Which mathematical framework would be most appropriate for solving this network restructuring problem?

A quality control manager needs to determine the probability that a batch of products meets specifications, given that individual components have known failure rates and the final product requires all components to function properly. Historical data shows that Component A fails 3% of the time, Component B fails 5% of the time, and Component C fails 2% of the time, with failures occurring independently. Which approach should be used?

A project manager must allocate a team of 12 specialists among 4 different projects, where each specialist has different skill ratings for each project type, and each project has minimum staffing requirements and maximum budget constraints. The objective is to maximize overall project success probability based on team composition. Which analytical approach is most suitable?

A manufacturing company must decide between expanding its current facility or building a new plant. The expansion costs $2.8 million upfront and increases capacity by 40%, while the new plant costs $5.2 million and doubles capacity. Both options involve 10-year financing at different rates, and market demand growth is uncertain. The decision must account for construction time, financing costs, and demand uncertainty. What analytical approach is most appropriate?

A insurance company is developing a new policy and needs to set premium rates based on customer risk profiles. They have historical claims data for 10,000 customers, including age, driving record, location, and claim amounts. The company wants to predict claim probability for new customers and set premiums that ensure profitability while remaining competitive.

Which mathematical framework would be most appropriate for developing this pricing model?

A small electronics manufacturer produces two models of wireless speakers: the Standard model and the Premium model. The company has constraints on labor hours, materials, and storage space. The Standard model requires 2 hours of labor and 3 units of materials per unit, while the Premium model requires 4 hours of labor and 2 units of materials per unit. The company has 240 labor hours and 180 units of materials available per week. Storage capacity allows for at most 80 units total. The Standard model generates $15 profit per unit, and the Premium model generates $25 profit per unit. Additionally, market research shows that the probability of selling any given Premium unit is 0.7, while Standard units always sell.

To maximize expected weekly profit, which mathematical approach would be most appropriate for this scenario?

A company manufactures two types of furniture, chairs and tables. Each chair requires 2 hours of carpentry and 1 hour of finishing. Each table requires 3 hours of carpentry and 2 hours of finishing. The company has 120 hours of carpentry and 70 hours of finishing available each week. The profit is $30 per chair and $50 per table. The company wants to determine the number of chairs and tables to produce each week to achieve the greatest possible profit. Which of the following methods is most appropriate to solve this problem?

A couple is taking out a $300,000 loan to purchase a house. The loan has a term of 30 years with a fixed annual interest rate of 6%, compounded monthly. They want to calculate their required monthly payment to pay off the loan in exactly 30 years. Which mathematical tool is specifically designed for this type of problem?

An electronics company has two manufacturing plants, A and B, and three distribution centers, X, Y, and Z. Plant A can produce 1,000 units and Plant B can produce 1,500 units per week. Centers X, Y, and Z require 800, 900, and 600 units, respectively. The shipping costs from each plant to each center are known. The company's goal is to determine how many units to ship from each plant to each distribution center to meet all demand while minimizing the total shipping cost. Which method should be used?

An island's economy consists of two sectors: agriculture (A) and tourism (T). To produce $1 of output, the agriculture sector requires $0.20 of its own products and $0.30 of tourism services. To produce $1 of output, the tourism sector requires $0.10 of agricultural products and $0.25 of its own services. There is an external demand for $50 million in agriculture and $80 million in tourism. To determine the total production level required from each sector to meet both internal and external demand, which method is the most direct?

A nutritionist is designing a dietary supplement using a blend of two ingredients, X and Y. Each ounce of X provides 20 units of vitamin A and 10 units of vitamin C. Each ounce of Y provides 15 units of vitamin A and 30 units of vitamin C. The supplement must provide at least 150 units of vitamin A and 180 units of vitamin C per serving. The costs of the ingredients are known. The goal is to find the amount of each ingredient that meets these nutritional requirements at the lowest possible cost. What is the most appropriate mathematical framework for this problem?

A public health official is modeling the progression of a non-lethal virus in a closed population. Individuals are classified as either Susceptible (S), Infected (I), or Recovered (R). Each week, known percentages of people transition between these states (e.g., 10% of Susceptible people become Infected, 50% of Infected people Recover, etc.). To predict the percentages of the population in each category several months in the future, which tool is most effective?

A factory produces light bulbs with a historical defect rate of 3%. A quality control manager selects a random sample of 20 bulbs for testing. The manager wants to determine the probability that exactly one bulb in the sample is defective. Which mathematical method is the correct one to use?

A city's parks department has a budget of $500,000 for new projects. They are considering five potential projects, each with a specific cost and a calculated 'community benefit score.' The department cannot fund projects partially; a project must be fully funded or not at all. The goal is to select the combination of projects that provides the maximum total community benefit score without exceeding the budget. Which method is best suited for this decision-making process?

An individual plans to save for retirement by depositing $500 at the end of each month into an account that pays 4.8% annual interest, compounded monthly. To calculate the total amount of money that will be in the account after 25 years, which of the following is the most suitable method?

A charity lottery sells 10,000 tickets. There is one grand prize of $5,000, five second prizes of $500, and twenty third prizes of $100. To determine if a ticket is a worthwhile purchase on average, a statistician wants to calculate the average payout per ticket. What method is most suitable for this calculation?

Urban planners are studying population shifts between a city's downtown, suburbs, and rural areas. Each year, a fixed percentage of residents from each area moves to the other two areas. For example, 10% of downtown residents move to the suburbs and 5% move to rural areas. To predict the population distribution in the long run, assuming these trends continue, which mathematical approach should be used?

A game consists of two stages. First, a fair six-sided die is rolled. If the result is even, the player draws one marble from Bag A. If the result is odd, the player draws one marble from Bag B. Bag A contains 3 red and 7 blue marbles. Bag B contains 6 red and 2 blue marbles. To find the overall probability that a player draws a red marble, which approach is most appropriate?

A company is evaluating whether to lease or purchase equipment worth $150,000. The lease option requires monthly payments of $3,200 for 5 years with no residual value. The purchase option requires a down payment of $30,000 and financing the remainder at 6.5% annual interest with monthly payments over 5 years, after which the equipment will have a residual value of $25,000. Which method should be used to make this decision?