Rocco's Pasta Bar makes manicotti according to an old family recipe which states M = min{3/2C, 3P}, where M, C, and P are pounds of manicotti, cheese, and pasta respectively.If cheese costs $3 per pound and pasta costs $1 per pound, how much would it cost to produce 10 pounds of manicotti in the cheapest way possible?
A)$3.33
B)$20
C)$23.33
D)$35
E)$10

Question

Quizplus · Accepted Answer

From the recipe, we know that for every pound of manicotti, we need 1 pound of cheese and 3/2 = 1.5 pounds of pasta. Therefore, for 10 pounds of manicotti, we need:
- 10 pounds of cheese at $3 per pound = $30
- 15 pounds of pasta at $1 per pound = $15
Total cost = $30 + $15 = $45
However, we can also try to minimize the cost by using the minimum amount of cheese required. From the recipe, we need 1 pound of cheese for every pound of manicotti, so if we only use 5 pounds of cheese instead of 10, we only need:
- 5 pounds of cheese at $3 per pound = $15
- 7.5 pounds of pasta at $1 per pound = $7.5
Total cost = $15 + $7.5 = $22.5
Therefore, the cheapest way to produce 10 pounds of manicotti is to use 5 pounds of cheese and 7.5 pounds of pasta, which costs $22.5. The answer is choice C.

Rocco's Pasta Bar Makes Manicotti According to an Old Family