Use the simplex method to solve this problem. A company manufactures 3-speed, 5-

Question

Use the simplex method to solve this problem. A company manufactures 3-speed, 5-speed, and 10-speed bicycles. Each through three departments: fabrication, painting and plating, and final assembly. The relevant manufacturing data is given in the table below. (a) How many bicycles of each type should the company manufacture per day in order to maximize profit? What is the maximum profit? (b) Discuss the effect on the solution to part (A) if the profit on a 10-speed bicycle increases to $110 and all other data remains the same. (c) Discuss the effect on the solution to part (A) if the profit on a 5-speed bicycle increases to $110 and all other data remains the same.

Explanation / Answer

a)

b)

It does effect on the final solution has the allowable increase is 0 in th solution.

c)

Allowable increase of 5 speed is upto 36.67 (i.e. 70+36.67 = 106.67). So even if we increase the profit to 110 the final solution change

Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$3 3 -speed 14.54545455 0 80 36.66666667 0 $C$3 5-speed 19.09090909 0 70 36.66666667 0 $D$3 10-speed 0 0 100 0 1E+30 Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$6 Fabricaton Constraints 120 10 120 16.66666667 42 $F$7 Painting and plating Constraints 130 10 130 7.142857143 40 $F$8 Final assembly Constraints 115.4545455 0 120 1E+30 4.545454545

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