Theobald's new Mediterranean diet requires that all his food come from one of the four "basic food groups", namely, Greek salad, figs, red wine, and...

Theobald, being an enterprising young man, has been taking a course in Operations Research and has formulated an LP problem to help him minimize his daily food costs. He solved the LP problem using LINDO and obtained the following output:

LP OPTIMUM FOUND AT STEP 2

OBJECTIVE FUNCTION VALUE

1) 9.000000

VARIABLE VALUE REDUCED COST

GS 0.000000 2.750000

FG 3.000000 0.000000

RW 1.000000 0.000000

CH 0.000000 5.000000

ROW SLACK OR SURPLUS DUAL PRICES

2) 250.000000 0.000000

3) 0.000000 -0.250000

4) 0.000000 -0.750000

5) 5.000000 0.000000

NO. ITERATIONS= 2

RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES

VARIABLE CURRENT ALLOWABLE ALLOWABLE

COEF INCREASE DECREASE

GS 5.000000 INFINITY 2.750000

FG 2.000000 1.833333 0.500000

RW 3.000000 1.000000 3.000000

CH 8.000000 INFINITY 5.000000

RIGHTHAND SIDE RANGES

ROW CURRENT ALLOWABLE ALLOWABLE

RHS INCREASE DECREASE

2 500.000000 250.000000 INFINITY

3 6.000000 4.000000 2.857143

4 10.000000 INFINITY 4.000000

5 8.000000 5.000000 INFINITY

Using the above information, answer the following questions:

a) What is the formulation of the LP problem that Theobald must have used?

b) What is Theobald's optimal daily diet and how much does it cost?

c) If a serving of Greek salad were to cost $3, rather than the current $5, what would be the new optimal daily diet and how much would it cost?

d) If a bottle of red wine were to cost $3.50, rather than the current $3, what would be the new optimal daily diet and how much would it cost?

e) By how much would the price of a bar of chocolate have to fall before it would become optimal for Theobald to consume some chocolate in his diet?