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 the table below. Bar Amount of Sugar (Ounces) Amount of Chocolate (Ounces) Profit (Cents) 1 2 7 2 3 1 5 If 50 oz of sugar and 100 oz of chocolate are available, after defining xi to be the number of Type i candy bars manufactured, Sugarco should solve the following LP: max z = 3x + 7x2 + 5x3 s.t. x1 + x2 + x3 = 50 2x + 3x2 + x3 = 100 X1, X2, X3 20 (Sugar constraint) (Chocolate constraint) After adding slack variables s1 and 52, the optimal tableau is as given below. Basic Variable Z X1 X2 X3 S NO rhs 3 0 0 4 300 Z -In 0 25 0 0 300 X'z = 25 X2 = 25 1 0 25 Using this optimal tableau, answer the following questions: d) For what values of Type 2 candy bar profit would the current basis remain optimal? e) If the profit for a Type 2 candy bar were 130, then what would be the new optimal solution to Sugarco's problem? f) For what amount of available sugar would the current basis remain optimal? g) If 60 oz of sugar were available, what would be Sugarco's profit? How many of each candy bar should the company make? h) If a Type 1 candy bar used 0.5 oz of sugar and 0.75 oz of chocolate, would the current basis remain optimal? i) 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? j) Sugarco is considering making Type 4 candy bars. A Type 4 candy bar earns 170 profit and requires 3 oz of sugar and 4 oz of chocolate. Should Sugarco manufacture any Type 4 candy bars? k) Find the shadow prices for the Sugarco constraints. 1) Use shadow prices to find Sugarco's profit if 40 oz of sugar were available