Rocco's Pasta Bar makes manicotti according to an old family recipe which states M = min{5/4C, 5P}, where M, C, and P are pounds of manicotti, cheese, and pasta respectively.If cheese costs $3 per pound and pasta costs $4 per pound, how much would it cost to produce 20 pounds of manicotti in the cheapest way possible?
A)$64
B)$48
C)$16
D)$33.33
E)$20

Question

Quizplus · Accepted Answer

The formula for making manicotti is given as $M = \min\{5C, 5P\}$, where $M$ is the pounds of manicotti, $C$ is the pounds of cheese, and $P$ is the pounds of pasta. To produce manicotti in the cheapest way possible, we need to find the minimum cost between using cheese and using pasta.Given that cheese costs $3 per pound and pasta costs $4 per pound, we need to determine the cost for producing 20 pounds of manicotti.1. Using cheese ($5C$): To produce 20 pounds of manicotti, we need $20/5 = 4$ pounds of cheese. The cost would be $4 \times $3 = $12$.2. Using pasta ($5P$): To produce 20 pounds of manicotti, we need $20/5 = 4$ pounds of pasta. The cost would be $4 \times $4 = $16$.The cheapest way to produce 20 pounds of manicotti is by using cheese, which costs $12. However, none of the provided options match this calculation. It seems there might have been a misunderstanding in the interpretation of the formula or the calculation process. Given the options and the calculations, none directly match the expected outcome based on the provided formula and costs. The correct approach would involve minimizing the cost based on the given prices and formula, but the provided options do not align with the calculated cost of $12. Therefore, there might be a mistake in the calculation or interpretation of the question as presented.

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