The Ozark Farm has $20,000$ broilers that are fed for $8$ weeks before being marketed.

The weekly feed per broiler varies according to the following schedule:

Week $12345678$

lb$/$broiler $\mathrm{.}26\mathrm{.}48\mathrm{.}751\mathrm{.}001\mathrm{.}301\mathrm{.}601\mathrm{.}902\mathrm{.}10$

For the broiler to reach a desired weight gain in $8$ weeks, the feedstuffs must satisfy

specific nutritional needs. Although a typical list of feedstuffs is large, for simplicity

we will limit the model to three items only: limestone$,$ corn, and soybean meal. The

nutritional needs will also be limited to three types: calcium, protein, and fiber. The

following table summarizes the nutritive content of the selected ingredients together

with the cost data.

Content $($lb$)$ per lb of

Ingredient Calcium Protein Fiber $ per lb

Limestone $\mathrm{.}380\mathrm{.}00\mathrm{.}00\mathrm{.}12$

Corn $\mathrm{.}001\mathrm{.}09\mathrm{.}02\mathrm{.}45$

Soybean meal $\mathrm{.}002\mathrm{.}50\mathrm{.}081\mathrm{.}60$

The feed mix must contain at least $\mathrm{.}8\%$ but not more than $1\mathrm{.}2\%$ calcium, at least $22\%$

protein, and at most $5\%$ crude fiber.

Solve the LP for week $1$ and then use post$-$optimal analysis to develop an optimal

schedule for the remaining $7$ weeks.