Alex’s questions

Question

For a given week, Trey's Coffee House has available 1728

 ounces of A grade coffee and 1760

 ounces of B grade coffee. These are blended into 1

-pound packages as follows: an economy blend that contains 2

 ounces of A grade coffee and 10

 ounces of B grade coffee, and a superior blend that contains 9

 ounces of A grade coffee and 2

 ounces of B grade coffee. (The remainder of each blend is made of filler ingredients.) There is a $6

 profit on each economy blend package sold and a $1

 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of each blend should it make to maximize its profit for the week?

Answer 1

Let x be the number of economy packages and y be the number of superior packages.

Profit = P(x,y) = 6x + 1y

If you plot 2x + 9y ≤ 1728 and 10x+2y ≤1760 on something like Desmos, you will see a trapezoid-like shape within the overlapped areas. The four corners of this shape are:

(0,192)

(144,160)

(176,0)

(0,0)

Calculating the profit for these points.

P(0,192) = 6(0)+1(192) = 192

P(144,160) = 6(144)+1(160) = 1024

P(176,0) = 6(176)+ 1(0) = 1056

P(0,0) = 0

So the most profit would be to make only 176 economy packages.