Nutrition: A cat food manufacturer uses fish and beef by-products. The fish contains 12 g of protein and 3 g of fat per ounce. The beef contains 6 g of protein and 9 g of fat per ounce. Each can of cat food must contain at least 60 g of protein and 45 g of fat. Find a system of inequalities that describes the possible number of ounces of fish and beef that can be used in each can to satisfy these minimum requirements. Graph the solution set. Find its vertices.

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MandyK514264 MandyK514264 · Answer 1 · 2022-10-25T10:40:45+02:00

A cat food manufacturer uses fish and beef by-products.

Let the number of ounces of fish = x

Let the number of ounces of beef = y

The fish contains 12 g of protein and 3 g of fat per ounce.

fish = 12x + 3y

The beef contains 6 g of protein and 9 g of fat per ounce.

Each can of cat food must contain at least 60 g of protein and 45 g of fat.

so,

[tex]\begin{gathered} 12x+6y\ge60 \\ 3x+9y\ge45 \end{gathered}[/tex]

Beside the above inequalities both of x and y must be greater than 0

so, the system of inequalities will be:

[tex]\begin{gathered} x\ge0 \\ y\ge0 \\ 12x+6y\ge60 \\ 3x+9y\ge45 \end{gathered}[/tex]

The following figure represents the solution of the system:

As shown in the graph, the vertices are:

( 0 , 10 ) , (3 , 4 ) , ( 15 , 0 )