A Turkey Ranch blends two different types of turkey feed, brand A and B$.$ Each feed type contains, in varying proportions, some or all of the three nutritional ingredients essential for fattening turkeys. Brand A feed costs the ranch $$0\mathrm{.}10$ per pound. Brand B costs $$0\mathrm{.}15$ per pound.

The rancher needs to determine the lowest$-$cost diet that meets the minimum monthly intake requirement for each nutritional component, in other words, he needs to establish the mix of pounds of each brand type to feed to the turkeys monthly. Turkeys need to get at least $45$ units of proteins per month, $24$ units of vitamins, and $1\mathrm{.}5$ units of iron.

The two brands of feed contain respectively: in terms of proteins $5$ units per pound $($brand A$)$ and $10$ units $($brand B$)$; vitamins $4$ units per pound $($A$)$ and $3$ units per pound $($B$)$; brand A contains $0\mathrm{.}5$ units of iron, but brand B has none. In any case, turkeys should not be fed more the $12$ pounds of feed in total.

$1.$ Based on the optimal solution you found, how many pounds of brand A$?$

brand B$?$

$2.$ What is the value of the objective function corresponding to your solution?

$3.$ Looking at the shape of the feasible region, how many corners are there?

$4.$ Using the sensitivity report you generate in excel, compute the allowable range for each of the objective function coefficients.

$5.$ What is the shadow price of the protein requirement?

$6.$ By looking at the sensitivity analysis what is the maximum iron requirement that would not change the optimal solution? $[$iron$]$

$7.$ Evaluate the problem if the vitamin constraints increase to $30$ units. Be mindful that depending on whether or not this is a binding constraint, the implications impact the optimal solution and the value of the objective function.

The new solution is $[$blank$]$ pounds of brand A and $[$blank$]$ pounds of brand B$.$ This has increased the optimal cost by $[$blank$]$ $ to a new total of $[$blank$]$ $$.$