$2.$ Kanine Health Inc. manufactures a variety of specialty dog foods sold through veterinarian offices. The foods are

designed to meet dietary needs for specific medical conditions. One particular mixture X$/$S is prepared for weight

reducing diets. It is a blend of chicken bi$-$products, lamb bi$-$products, wheat flour and rice flour.

Among the requirements for each $1$kg bag of X$/$S are that the amount of protein be at least $75$ grams, fat at most

$100$ grams, carbohydrates at least $80$ grams and fiber at least $30$ grams. The costs and relative amounts of each of

these properties per kilo of the $4$ foods are as follows:

The LP model for the problem is given as the follows. $\backslash (\backslash$mathrm$\{$C$\},\backslash$mathrm$\{$L$\},\backslash$mathrm$\{$W$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$R$\}\backslash )$ represent

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a$)$ Use Excel to solve the problem, and print out the LP model, optimal solution and the Sensitivity Report.

Now use the sensitivity report to answer the following questions. Each question is independent of the others.

b$)$ How much chicken, lamb, rice and wheat are used to make a $1$ kg bag of X$/$S$?$

c$)$ Suppose that the cost of Chicken increased to $$0\mathrm{.}90.$ Would the solution stay the same? How much can the

price of chicken change $($up or down$)$ and the solution remain unchanged?

d$)$ How low must the price of wheat be before you are enticed to use it in the mix?

e$)$ Suppose that the requirements for protein was increased from $75$ grams to $80$ grams. What would be the

increase in costs?

f$)$ If the fat content were allowed to be $120$ grams, what would be the cost?

g$)$ Kanine has been asked to have more than $30$ grams of Fiber in the food. How high would the Fiber

requirement be before Kanine would have to change the blend of foods?

h$)$ Suppose that Kanine was instructed to start using some wheat in the blend. What is the impact on costs for

every $100$ grams of wheat substituted in the blend?