West Coast Corporation is a manufacturer of industrial products. It produces 4 products A B C and D. The company wants to
determine the optimal mix for its products. The products use three different types of resources: Resource 1 Resource 2 and Resource 3. The product mix problem
is formulated as a resource allocation problem where the objective is to maximize total profit.

The sensitivity report is shown as follows where the shaded cells are to be determined.

The two tables below show the results of the Solver Table by varying the available supplies of Resources 2 and 3. Table I
shows the total profit for each combination of resource 2 and 3 supply. Table II shows the optimal number of
products of A B C and D to produce e.g. (003025) implies that the optimal number of A is 0 of B is 0 of C is 30 and of D is 25.

Table I

Table II

Answer the following questions:

a. Formulate the LP problem algebraically. Define the
decision variables the objective function and the constraints functional and non-negativity.

b. What is the optimal product mix that is how many
units of each product should be produced such that the total profit is maximized? What is the total profit for this optimal mix?

c. Given the information in the sensitivity report
find the values of the shaded cells (A B C and D).

d. Assume that you want to increase the unit profit
of Product A by $5 keeping the unit profits of the other products unchanged would the optimal solution change? How much would the total profit
change?

e. Given the information in the Solver Tables
determine a range estimate where the value for E is likely to lie (Since resource 2 is run in increments of 10 the range would be for
example between 140 and 150.)

f. Do the same thing for F.

g. Do the same thing for G.

h. Do the same thing for H.

i. Assume that management wants to increase the
available supply of only one of the resources by 5 units. Which resource should you choose to increase in order to get the biggest
increase in total profit? Justify your answer.

j. Assume you increase Resource 2 by 5 units and
decrease Resource 3 by 5 units simultaneously what is the change in total profit? Justify your answer.