Business 2400 – Decision Modeling Report Writing - Business Assignment Help

Assignment Task:

Task:

Instructions Questions 1 and 2 are to be done by hand, showing all the steps needed to derive the answers. [Of course, you could use LINGO or the Excel Solver to verify your answers, but this is not to be submitted.] Use Word or pdf for this question; if making the solutions with cursive writing, please be neat.
For Questions 3 and 4, a computer-based sensitivity analysis needs to be performed.
For each question, on LINGO you need a file for the model, the solution report, and the range report. For Excel, one file with nine tabs can be used; for each of the three questions, there is the model, the Answer Report, and the Sensitivity Report.

Use Word or pdf to give the answers to the sensitivity questions. For each give part, write a couple of sentences; don’t just submit a numerical answer.
1. (10 marks) Suppose that the objective of a two-variable optimization model is to maximize 14x1 + 18x2, and that we find by graphing that the binding constraints are:

(2) 7x1 +3x2 ≤ 516
(5) 5x1 +9x2 ≤ 780

Based on the above, the optimal solution is at x1 = 48, x2 = 60, and OFV = 1752.
(a) For the objective function coefficients, find the allowable increase and decrease for each coefficient (based on one-at-a-time changes).

(b) Suppose that the right-hand side of (2) is changed to 516+?b2. Find expressions for the values of x1, x2, and OFV as a function of ?b2, and from the latter state the shadow price of this constraint. [Do not worry about the allowable range.]

2. (a) (45 marks) Solve the following model graphically, using a 50 by 50 grid.

maximize 4x1 + 9x2
subject to
(1) 15x1 + 3x2 ≤ 450
(2) 40x1 + 10x2 ≥ 400
(3) 10x1 + 8x2 ≤ 420
(4) 4x1 + 20x2 ≤ 588
x1 , x2 ≥ 0

(b) Perform a sensitivity analysis for each of the objective function coefficients.

(c) Perform a sensitivity analysis for the right-hand-side values for each of the non- binding constraints.

(d) Perform a sensitivity analysis for the right-hand-side values for each of the two binding constraints.
(e) For each of the two binding constraints, find the change to each variable as function of the right-hand side value, and from these relationships calculate the two shadow prices.

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