Oz makes lion food out of giraffe and gazelle meat. Giraffe meat has 16 grams of protein and 32 grams of fat per pound, while gazelle meat has 32 grams of protein and 16 grams of fat per pound. A batch of lion food must contain at least 25,600 grams of protein and 38,400 grams of fat. Giraffe meat costs $1 per pound and gazelle meat costs $2 per pound. How many pounds of each should go into each batch of lion food in order to minimize costs

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calculista calculista · Answer 1 · 2019-08-14T16:42:56+02:00

Answer:

To minimize costs, the pounds of giraffe meat are 1,067 and the pounds of gazelle meat are 267.

Step-by-step explanation:

Let

x -----> pounds of meat of giraffe

y -----> pounds of meat of gazelle

we know that

[tex]16x+32y \geq 25,600[/tex] -----> inequality A

[tex]32x+16y \geq 38,400[/tex] -----> inequality B

[tex]C=x+2y[/tex] ----> the function cost

using a graphing tool

The solution of the system of inequalities is the shaded area (positive values of x and y between the two solid lines)

see the attached figure

Three vertices of the shaded area are (0,2,400), (1,067,267) and (1,600,0)

Substitute in the function cost and then compare the results

For (0,2,400)

[tex]C=0+2(2,400)=\$4,800[/tex] ---> It doesn't make sense, because lion food should contain giraffe meat and gazelle meat.

For (1,067,267)

[tex]C=1,067+2(267)=\$1,601[/tex]

For (1,600,0)

[tex]C=1,600+2(0)=\$1,600[/tex] ---> It doesn't make sense, because lion food should contain giraffe meat and gazelle meat.

therefore

To minimize costs, the pounds of giraffe meat are 1,067 and the pounds of gazelle meat are 267.