Practice Test 12

A bakery makes muffins and cookies. Let $x$ be the number of muffin batches and $y$ be the number of cookie batches.

Constraints:

• Each muffin batch takes 2 hours and each cookie batch takes 3 hours.
• The bakery has at most 18 hours available.
• Each muffin batch uses 4 cups of flour and each cookie batch uses 2 cups of flour.
• The bakery has at most 24 cups of flour.
• $x\ge 0$ and $y\ge 0$.

Which constraints does the point $(x,y)=(6,2)$ violate?

A community center offers two types of classes: yoga and art. Let $x$ be the number of yoga classes and $y$ be the number of art classes scheduled in a week.

Constraints:

• The center has at most 20 total class slots: $x+y\le 20$.
• Yoga classes require at least 6 sessions: $x\ge 6$.
• Art classes cannot exceed 12 sessions: $y\le 12$.
• $x\ge 0$ and $y\ge 0$.

Determine if each solution is viable or nonviable: (i) $(6,12)$, (ii) $(10,11)$, (iii) $(5,10)$.