3 Consider the diet problem discussed in Section 3.4. Use the LINDO output in Figure 8 to answer the following questions.

a If a Brownie costs 30¢, then what would be the new optimal solution to the problem?

b If a bottle of cola cost 35¢, then what would be the new optimal solution to the problem?

c If at least 8 oz of chocolate were required, then what would be the cost of the optimal diet?

d If at least 600 calories were required, then what would be the cost of the optimal diet?

e If at least 9 oz of sugar were required, then what would be the cost of the optimal diet?

f What would the price of pineapple cheesecake have to be before it would be optimal to eat cheesecake?
g What would the price of a brownie have to be before it would be optimal to eat a brownie?
h Use the SLACK or SURPLUS portion of the LINDO output to determine the allowable increase and allowable decrease for the fat constraint. If 10 oz of fat were required, then would the optimal solution to the problem change?

LINDO Output for Diet Problem 50 BR +20 IC + 30 COLA + 80 PC MAX SUBJECT TO 400 BR 200 IC +150 COLA + 500 PC >= 500 2) 3) 3 BR + 2 IC >= 6 4) 2 BR +2 IC + 4 COLA +4 PC >= 10 5) 2 BR +4 IC + COLA + 5 PC >= 8 END LP OPTIMUM FOUND AT STEP 2 OBJECTIVE FUNCTION VALUE 90.0000000 1) VARIABLE VALUE BR .000000 IC 3.000000 COLA 1.000000 PC .000000 REDUCED COST 27.500000 .000000 .000000 50.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 3) 250.000000 .000000 .000000 -2.500000 4) 5) .000000 5.000000 2 -7.500000 .000000 NO. ITERATIONS= RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT COEF BR 50.000000 IC 20.000000 COLA 30.000000 PC 80.000000 ALLOWABLE INCREASE INFINITY 18.333330 10.000000 INFINITY RIGHTHAND SIDE RANGES ALLOWABLE DECREASE 27.500000 5.000000 30.000000 50.000000 ROW CURRENT RHS 2 500.000000 3 6.000000 4 10.000000 ALLOWABLE ALLOWABLE INCREASE DECREASE 250.000000 INFINITY 4.000000 2.857143 INFINITY 4.000000 5 8.000000 5.000000 INFINITY