PLEASE ANSWER ONLY ONE (a)

2. Sugarco can manufacture three types of candy bar. Each candy bar consists totally of sugar and chocolate. The compositions of each type of candy bar and the profit earned from each candy bar are shown in table below. Bar 1 2 3 Amount of sugar (ounces) 1 1 1 Amount of chocolate (ounces) 2 3 1 Profit (Cents) 3 7 5 Fifty oz of sugar and 100 oz of chocolate are available. After defining x; to be the number of Type i candy bars manufactured, Sugarco should solve the following LP: a. Solve the LP using simplex method. max z = 3x1 + 7x2 + 5x3 s.t; x1 + x2 + x3 s 50 (Sugar constraint) 2x1 + 3x2 + x3 = 100 (Chocolate constraint) x1, x2, x3 > 0 b. Solve the LP using GAMS. c. After you solve the LP using simplex method, you will obtain the optimal tableau below: Z x1 x2 x3 s1 s2 rhs 3 1 0 0 0 0 1 1/2 0 1 0 4 3/2 -1/2 Basic Variable z=300 x3= 25 x2 = 25 300 25 25 -1/2 1/2 1/2 Using this optimal tableau, answer the following questions: i. For what values of Type 1 candy bar profit does the current basis remain optimal? If the profit for a Type 1 candy bar were 7, what would be the new optimal solution to Sugarco's problem? ii. For what values of Type 2 candy bar profit would the current basis remain optimal? If the profit for a Type 2 candy bar were 13, then what would be the new optimal solution to Sugarco's problem? iii. For what amount of available sugar would the current basis remain optimal? iv. If 60 oz of sugar were available, what would be Sugarco's profit? How many of each candy bar should the company make? Could these questions be answered if only 30 oz of sugar were available? v. Suppose a Type 1 candy bar used only 0.5 oz of sugar and 0.5 oz of chocolate. Should Sugarco now make Type 1 candy bars? vi. Sugarco is considering making Type 4 candy bars. A Type 4 candy bar earns 17 profit and requires 3 oz of sugar and 4 oz of chocolate. Should Sugarco manufacture any Type 4 candy bars? d. Use the GAMS output you find to answer the questions i., ii., iii., iv. and v. in part c. Interpret your answers