$1)(2$ pts$)$ A poultry farmer is considering purchasing a mixture of two chicken feeds. The final mixture of chicken feed must contain at least $60$ grams of protein, at least $8$ grams of fat, and at most $180$ grams of carbohydrate. The cost $($per ounce$)$ and the nutrition information $($per ounce$)$ are shown below:

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Cost

Protein

Fat

Carbohydrate

Feed A

$$7$

$12$ grams

$2$ grams

$16$ grams

Feed B

$$5$

$6$ grams

$1$ grams

$18$ grams

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In order to minimize cost, how many ounces of feed A and feed B should the farmer purchase?

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d$)$ Test all the corner points and determine the optimal solution that minimizes cost to the farmer.