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Promber if (15 Poiash. Ziba, ine. manufactares Tianium and Carbon frume nacquets. In the orming prodiction: period, Zibu neads to decide bow many of each type of nequets should be produced in order to maximitie profi. Fach racquet goes through two prodaction processes, Each Titanium frame requires 21 minutes of process I time ind 15 minates of process II time. Each Carben frame requires 15 minutes of process I time and 20 minutes of process II time. In the upooming production period, at least 27 bours are available in process I and es more than 40 houn are avaifable in process in. In the upcoming period the decnand for the Titaniam frames is estimated in be at leat 60 units. Due to a decline in the demand for Carbon frames, the company does not want to produce more than 45 Carbon frame nequets. Furthermore, management has decided that the production of the number of Carbon frames shorld be at least 20% of total production. Fach Titanium racquet costs 588 to produce and sclls for $200. Each Carbon frame racquet costs $70 to produce and sells for $170. a. Formulate an UP probleen to determine the highest profir. Write your problem formulafion. Let your decision variables be: 5.X]= Number of Titanium frame racquets to produce X2 = Number of Carboe frame racquets to produce b. Graph the constraints and identify the region of feasible solations. 9 Using the grephical precedure, solve the problem. 10 How many of each type of racquets should be produced and, what will be the maximum profit? 11 Are there any slack or surphises at optimum? What are they, and what are their values? 12. c. If the production costs of Titanium frame racquets were increased to $125 per unit, what would be the optimum solutioa? Is there more than one optimum solution to the new problem? If yes, give at least two optimum solutions 13 and their respective slacks and or surpluses