Use this question $25$ to answer question $10$ Sanderson Manufacturing produces ornate, decorative wood frame doors and win$-$ dows. Each item produced goes through three manufacturing processes: cutting, sanding, and finishing. Each door produced requires $1$ hour in cutting, $30$ minutes in sanding, and $30$ minutes in finishing. Each window requires $30$ minutes in cut$-$ ting, $45$ minutes in sanding, and $1$ hour in finishing. In the coming week Sander$-$ son has $40$ hours of cutting capacity available, $40$ hours of sanding capacity, and $60$ hours of finishing capacity. Assume all doors produced can be sold for a profit of $$500$ and all windows can be sold for a profit of $$400.$

a$.$ Formulate an LP model for this problem b$.$ Sketch the feasible region.

c$.$ What is the optimal solution?

Use Solver to create Answer and Sensitivity Reports for question $25$ at the end of

chapter $2$ and answer the following questions:

a$.$ If the profit on doors increased to $$700$ would the optimal solution change?

b$.$ If the profit on windows decreased to $$200$ would the optimal solution change?

c$.$ Explain the shadow price for the finishing process.

d$.$ If $20$ additional hours of cutting capacity became available how much additional

profit could the company earn?

e$.$ Suppose another company wanted to use $15$ hours of Sanderson's sanding

capacity and was willing to pay $$400$ per hour to acquire it$?$ Should Sanderson

agree to this? How $($if at all$)$ would your answer change if the company instead

wanted $25$ hours of sanding capacity?

Use this question $25$ to answer question $10$ Sanderson Manufacturing produces ornate, decorative wood frame doors and win$-$ dows. Each item produced goes through three manufacturing processes: cutting, sanding, and finishing. Each door produced requires $1$ hour in cutting, $30$ minutes in sanding, and $30$ minutes in finishing. Each window requires $30$ minutes in cut$-$ ting, $45$ minutes in sanding, and $1$ hour in finishing. In the coming week Sander$-$ son has $40$ hours of cutting capacity available, $40$ hours of sanding capacity, and $60$ hours of finishing capacity. Assume all doors produced can be sold for a profit of $$500$ and all windows can be sold for a profit of $$400.$

a$.$ Formulate an LP model for this problem b$.$ Sketch the feasible region.

c$.$ What is the optimal solution?