5. (9 points)A salad dressing supplier has been using Linear Programming for years to determine how much salad dressing they should plan to produce for every season. In particular, they specialize in producing three kinds of salad dressing: Dijon, Classic Vinaigrette, and Roasted Garlic. All these dressings require some use of olive oil to produce. Taking this into account, the management team has formulated the following LP model that determines the optimal amount they should produce for each dressing.

X1 : the amount of Dijon

X2 : the amount of Classic Vinaigrette

X3 : the amount of Roasted Garlic

The problem was formulated (in LINGO-style) as follows:

Max = 1.2*X1 + 1.6*X2 + 1.4*X3;

6*X1 + 5*X2 +3*X3 <=300; (C1:Olive ol-liters)

9*X1 + 4*X2 + 5*X3 <=280; (C2: Labour minutes)

2*X1 +8*X2 +4*X3 <=320; (C3:Machine- minutes)

X1>=0; C4:Nonnegative

X2>=0; C5: Nonnegative

X3>=0; C6: Nonnegative

Global optimal solution found.

Objective value: 88.00000

Infeasibilities: 0.000000

Total solver iterations: 3

Elapsed runtime seconds: 0.10

Variable Value Reduced Cost

X1 0.000000 0.8000000

X2 20.00000 0.000000

X3 40.00000 0.000000

Row Slack or Surplus Dual Price

1 88.00000 1.000000

2 80.00000 0.000000

3 0.000000 0.2000000

4 0.000000 0.5000000

5 0.000000 0.000000

6 20.00000 0.000000

7 40.00000 0.000000

Objective Coefficient Ranges:

Current Allowable Allowable

Variable Coefficient Increase Decrease

X1 1.200000 0.8000000 INFINITY

X2 1.600000 0.7384615 0.4800000

X3 1.400000 0.6000000 0.3000000

Righthand Side Ranges:

Current Allowable Allowable

Row RHS Increase Decrease

2 300.0000 INFINITY 80.00000

3 280.0000 120.0000 120.0000

4 320.0000 147.6923 96.00000

5 0.000000 0.000000 INFINITY

6 0.000000 20.00000 INFINITY

7 0.000000 40.00000 INFINITY

EXPLAIN ALL ANSWERS IN A SINGLE SHORT SENTENCE EACH.

(1) (1 point)For maximum profit contribution, how much of each product should be produced? How much contribution selling the output will make?

(2) (1 point) Which constraints are binding, i.e., are satisfied as equations?

(3) (1 point) How manyOlive oilused in the suggested plan and how many is left over? Suppose we have moreolive oilfrom 300unitsto 000(last 3 digits of your student id)units. How will this change influence the solution?

1. (1 point) Why noDijon is included in optimal solution? Explain it with reduced cost/opportunity cost.

(5) (1 point) Customers would be prepared to pay an additional 0.5 forClassic Vinaigrette. Would such a price increase change the optimal solution? Why?

(6) (1 point) What will happen to the optimal solution if the price ofClassic Vinaigrette increases by $0.25, and the price ofRoasted Garlicdecreases by $0.25 at same time?

(7) (1 point) What is the dual price for the constraint 2 for Labor? What does it indicate?

(8) (1 point)What will happen to optimal result if we have more labor time from 280 minutes to 500 minutes.

(9) (1 point) The Company considers adding extra machine time with $0.AA(AA is the last two digit of your student id) per minute.What will happen to our profit? How about $BB(The 3^rd and 4th digits of your student id) per minute?