NEVERSTICK ALUMINUM COOKWARE $(25$ POINTS$).$ Neverstick Aluminum Cookware produces a line of

nonstick cookware made of hard$-$anodized aluminum and a durable nonstick surface. During the next production

period they are considering producing three items in their line: the frypan, wok, and stockpot. Each item must go

through the two stages of production $($molding and assembly$),$ and requires a certain amount of aluminum. They have

formulated a linear program to determine the production levels that would maximize their profit. The solved

spreadsheet model and corresponding sensitivity report are shown below.

Variable Cells

Constraints

For each of the following problems, answer the question as specifically and completely as is possible without re$-$

solving the problem with the Solver. Type your answers directly into spreadsheet tab $1,$ answering in the space

provided for each problem part. All problems are independent $($i$.$e$.,$ any change made in one problem part does not

apply for the other problem parts$).$ For full credit, you must justify your answers by utilizing the results in the

sensitivity report $($e$.$g$.,$ indicate what number was used in the sensitivity report to justify your answer$).$

a$.$ Suppose the profit per wok increases from $$12\mathrm{.}30$ to $$14\mathrm{.}80.$ Will this change the optimal production quantities?

What can be said about the change in total profit?

b$.$ Suppose the profit per frypan decreases by $$1$ and the profit per wok increases by $$2.$ Will this change the optimal

production quantities? What can be said about the change in total profit?

c$.$ Suppose a worker in the molding department calls in sick, so that now eight fewer hours are available in the

molding department. How much would this affect total profit? Would it change the optimal production

quantities?

d$.$ Suppose one of the workers in the molding department is also trained to do assembly. Would it be a good idea to

have this worker shift some of her time from the molding department to the assembly department? Indicate the

rate at which this would increase or decrease total profit per minute shifted. How many minutes can be shifted

before this rate might change?

e$.$ The allowable decrease for the stockpot objective coefficient and for the aluminum constraint were both

mistakenly deleted from the sensitivity report. Based on the nature of the solution, you should be able to infer

what numbers were there. For each, indicate what number should be there and, in a sentence or two, explain the

intuition as to why you know that particular number should be there.