Rocco's Pasta Bar makes manicotti according to an old family recipe which states M = min{ , 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?

Question

Rocco's Pasta Bar makes manicotti according to an old family recipe which states M = min{  , 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?

Quizplus · Accepted Answer

We are given the formula M = min{11C, 3P} and need to produce 10 pounds of manicotti in the cheapest way possible.

Let's consider the two scenarios separately:

Scenario 1: Using 11 pounds of cheese (since that is the minimum between the two options in the formula)

M = 11C = 11(3) = $33

In this scenario, the cost of cheese alone is $33, which is too expensive to produce 10 pounds of manicotti.

Scenario 2: Using 3 pounds of pasta (since that is the minimum between the two options in the formula)

M = 3P = 3(1) = $3

In this scenario, the cost of pasta alone is only $3, which is the cheapest way to produce 10 pounds of manicotti. Therefore, the answer is C.

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