Question: 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

3 Consider the diet problem discussed in Section

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? 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? My diet requires that all the food I eat come from one of the four basic food groups (chocolate cake, ice cream, soda, and cheesecake). At present, the following four foods are available for consumption: brownies, chocolate ice cream, cola, and pineapple cheese- cake. Each brownie costs 50, each scoop of chocolate ice cream costs 20, each bottle of cola costs 30$, and each piece of pineapple cheesecake costs 80. Each day, I must in- gest at least 500 calories, 6 oz of chocolate, 10 oz of sugar, and 8 oz of fat. The nutri- tional content per unit of each food is shown in Table 2. Formulate a linear programming model that can be used to satisfy my daily nutritional requirements at minimum cost. FIGURE 8 LINDO Output for Diet Problem 500 MAX 50 BR + 20 IC + 30 COLA + 30 DC SUBJECT TO 21 400 BR + 200 IC + 150 COLA + 500 PC > 3) 3 RR + 2 4) 2 BR + 2 TC + 4 COLA + 4 PC 5) BR + 4 IC + COLA + 5 PC END 10 LP OPTIMUM FOUND AT STEP 2 OBJECTIVE FUNCTION VALUE 1) 90.0000000 REDUCED BOOT 27.500000 VARIABLE BB IC COLA PC VALJE .000000 3.000000 1.000000 .000000 .000000 50.000000 ROH 2) SLACK OR SURPLUS 250.000000 000000 000000 5.000000 DUAL PRICES .000000 - 2.500000 -7.500000 .000000 MO. ITERATIONS 2 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLONABLE ALLOWABLE INCREASE DECREASE BR 50.000000 INFINITY 27.500000 IC 20.000000 18.333330 5.000000 COLA 30.000000 10.000000 30.000000 PC NO.000000 INFINITY 50.000000 ROM 2 3 RIGHTHAND SIDE RANGES CURRENT ALLONABLE ALLOWABLE RHS INCREASE DECREASE 500.000000 250.000000 INFINITY 6.000000 4.000000 2.857143 10.000000 INFINITY 4.000000 8.000000 5.000000 INFINITY S

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