Problem T$5-8$

Brand $x$ animal feed is made from a combination of wheat and corn. Wheat contains $10$ percent protein, $40$ percent starch, and $50$ percent fiber by weight. Corn contains $15$ percent protein, $50$ percent starch, and $35$ percent fiber by weight. The recipe for brand $x$ feed calls for a minimum of $45$ percent starch and a minimum of $40$ percent fiber; there is no restriction on protein. If a batch of at least $800$ pounds of brand $x$ is produced, how many pounds of wheat and how many pounds co costs Wheat and corn combine in proportion to their weights when blended together to pro fiber. Wheat costs $$0\mathrm{.}03$ per pound, and corn costs $$0\mathrm{.}05$ cents per pound.

a$.$ What are blending constraints for this problem? $($Hint: There is one blending constraint for starch and another for fiber. Express the constraint in the $0$ format.$)($Use a negative sign to note any negative values. Round your answer to two decimal places where needed.$)$

Starch:

W

C $0$

Fiber:

w

C $0$

b$.$ What is the optimal solution using Excel Solver. How much wheat and corn is used, and what is the minimum cost?

$w=$

$C=$

Minimum cost $=$