Question

I post this question but C, G, and H was not answered...can I have an answer for them please as soon as possible.

Interpreting an LP output after solving the problem using the software. The following linear programming problem has been solved using the software. Use the output to answer the questions below LINEAR PROGRAMMING PROBLEM: MAX 25X1+30X2+15X3 1) 4X1+5X2+8X3<1200 2) 9x1+15X2+3X3<1500 OPTIMAL SOLUTION: Objective Function Value- 4700.000 ariabl X1 x2 X3 0s 0.000 10.000 0.000 140.000 0.000 80.000 Less afe Dual Prices 1.000 2.333 0.000 0.000 OBJECTIVE COEFFICIENT RANGES: Variable x1 X2 Lower Limit 19.286 No Lower Limit 8.333 Current Value 25.000 30.000 Upper Limit 45.000 40.000 X3 15.000 50.000 RIGHT HAND SIDE RANGES Lower Limit urrent Value pper Limit 1200.000 1500.000 666.667 450.000 4000.000 2700.000 2 Give the complete optimal solution. Give the reduced costs? Explain fully its meaning What is the dual price for the second constraint? What interpretation does this have? a. b. c. d. Over what range can the objective function coefficient of x2 vary before a new solution point becomes optimal? e. By how much can the amount of resource 2 decrease before the dual price will change? f. Which constraint(s) have a surplus ?Explain f. Which constraint(s) have a slack ? Explain h. What does the objective function value represent? (Give the breakdown to show how x1, x2 and x3 contribute to the objective function value).

Answer 1

c.

Dual price for second constraint is 2.333.

It means for every additional unit of increase/decrease of 2nd constraint, objective value will increase/decrease by 2.333

G.

Yes, this problem can be solved using graphical model. Additional constraints required are non-negativity constraints => X1 >= 0,X2>= 0 and X3>= 0

H.

Objective function value represents the value of the objective function after substituting X1,X2 and X3

Objective function value => 25X1+30X2+15X3 where X1 = 140, X2 = 0 and X3 = 80

so, Objective function value => 25*140 + 30*0 + 15*80 = 4700