Creative Kitchen Tools Manufactures a Wide Line of Gourmet Cooking $\le$

Essay

Creative Kitchen Tools manufactures a wide line of gourmet cooking tools from stainless steel. For the coming production period, there is demand of 1200 for 8 quart stock pots, and unlimited demand for 3 quart mixing bowls and large slotted spoons. In the following model, the three variables measure the number of pots, bowls, and spoons to make. The objective function measures profit. Constraint 1 measures steel, constraint 2 measures manufacturing time, constraint 3 measures finishing time, and constraint 4 measures the stock pot demand.
Max
5x₁ + 3x₂ + 6x₃
s.t.
3x₁ + 1x₂ + 2x₃ $\le$ 15000
4x₁ + 4x₂ + 5x₃ $\le$ 18000
2x₁ + 1x₂ + 2x₃ $\le$ 10000
x₁ $\le$ 1200
x₁, x₂, x₃ $\ge$ 0
The final tableau is: $$\begin{array} { c c | c c c ccc c | c } & & \mathrm { x } _ { 1 } & \mathrm { x } _ { 2 } & \mathrm { x } _ { 3 } & \mathrm {~s} _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 }& \mathrm {~s} _ { 4 } \\\text { Basis } & \mathrm { C } _ { \mathrm { B } } &5&3&6&0&0&0&0& \\\hline \mathrm {~s} _ { 1 } &0&0&-2&-1.75&0&-.75&0&0&1500\\ \mathrm {~s} _ { 4 }&0&0&1&1.25&0&.25&0&1&3300\\ \mathrm {~s} _ { 3 }&0&0&-1&-.5&0&-.5&1&0&1000\\ \mathrm { x } _ { 1 } &5&1&1&1.25&0&.25&0&0&4500\\\hline& \mathrm { z } _ { j }&5&5&6.25&0&1.25&0&0&22500\\&\mathrm{C}_{\mathrm{j}}-z_{\mathrm{j}}&0&-2&-.25&0&-1.25&0&0&\end{array}$$
a.Calculate the range of optimality for c₁, c₂, and c₃.
b.Calculate the range of feasibility for b₁, b₂, b₃, and b₄.
c.Suppose that the inventory records were incorrect and the company really has only 14000 units of steel.What effect will this have on your solution?
d.Suppose that a cost increase will change the profit on the pots to $4.62.What effect will this have on your solution?
e.Assume that the cost of time in production and finishing is relevant.Would you be willing to pay a $1.00 premium over the normal cost for 1000 more hours in the production department? What would this do to your solution?