Saba, Inc. manufactures Titanium and Carbon frame racquets. In the coming production period, Saba needs to decide how many of each type of racquets should be produced to maximize profit. Each racquet goes through two production processes. Each Titanium frame requires 21 minutes of process I time and 15 minutes of process II time. Each Carbon frame requires 15 minutes of process I time and 20 minutes of process II time. In the upcoming production period, at least 27 hours are available in process I and no more than 40 hours are available in process II. In the upcoming period the demand for the Titanium frames is estimated to be at least 60 units. Due to a decline in the demand for Carbon frames, the company does not want to produce more than 45 Carbon frame racquets. Furthermore, management has decided that the production of the number of Carbon frames should be at least 20% of total production. Each Titanium racquet costs $88 to produce and sells for $200. Each Carbon frame racquet costs $70 to produce and sells for $170.

a. Formulate an LP problem to determine the highest profit. Write your problem formulation below. Let your decision variables to be:

X1 = Number of Titanium frame racquets to produce

X2 = Number of Carbon frame racquets to produce

b. Graph the constraints and identify the region of feasible solutions. Using the graphical procedure,
solve the problem. How many of each type of racquets should be produced and what is the
maximum profit?

c. Are there any slack or surpluses at optimum? What are they and what are their values?

d. If the production costs of Titanium frame racquets were increased to $125 per unit, what would be
the optimum solution? Is there more than one optimum solution to the new problem?
If yes, give at least two optimum solutions and their respective slacks and or surpluses.