illustrative_exam2_solution

illustrative_exam2_solution - Illustrative Exam 2 1...

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Illustrative Exam 2 1 Solutions BUAD311 – Operations Management Fall 2011 Section A: Multiple Choices [No partial credits.] Circle only one. 1. Of the following five expressions, how many are linear? y x y x y x y x y x 2 5 2 5 2 5 3 log 3 2 + - - + - a) Only one expression. The other four are non-linear. b) Exactly two of them. The other three are non-linear. c) Exactly three. The other two are non-linear. d) Exactly four. The other is non-linear. e) All the five are. b) 2. Which of the following is(are) true? I: A linear program always has a feasible solution. II: A linear program always has some decision variable(s) III: A linear program always has a unique optimal solution IV: A linear program always has an objective function. a) I and II are true. The others are false. b) I and III are true. The others are false. c) III and IV are true. The others are false. d) II and IV are true. The others are false. e) II and III are true. The others are false. d) 1 These are all actual questions that appeared in past exams. Note we may be covering slightly different materials this semester. 1
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3. Our company produces two products, product X and product Y, using three inputs: labor, raw material A, and raw material B. One unit of product X requires 8 hours of labor, 5 pounds of A, and 7.5 pounds of B. One unit of product Y requires 6 hours of labor, 10 pounds of A, and 4.5 pounds of B. The demand of each product is so large that the company can sell as many as it can produce. The firm earns a profit of $3 per unit of X and $4 per unit of Y. However, only 1200 labor hours, 900 pounds of A, and 675 pounds of B are available to the firm each day. You formulated the problem as a linear program. Decision variables: x: #units of product X we produce y: #units of product Y we produce Maximize 3x + 4y Objective: maximize the profit function Subject to: 8x + 6y ≤ 1200 Labor hours constraint 5x + 10y ≤ 900 Raw Material A constraint 7.5x + 4.5y ≤ 675 Raw Material B constraint x ≥ 0, y ≥ 0 Non-negativity constraints The optimal decision variables turned out: x = 51.4285 and y = 64.2857. The sensitivity report created by Excel Solver is as follows. Ad u t ble Cells Final Reduced Objectiv e Allowable Allowable Cell Nam e Value Cost Coefficie nt Increase Decrease $B$ 1 x 51.4285 0 3 3.66666666 7 1 $B$ 2 y 64.2857 0 4 2 2.2 Constraints Final Shadow Constrai nt Allowable Allowable Cell Nam e Value Price R.H. Side Increase Decrease $E$ 3 797.142857 1 0 1200 1E+30 402.857142 9 $F$ 3 900 0.31428571 4 900 600 1E+30 $G$ 3 675 0.19047619 675 423 270 Which of the following statements is true? 2
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a) If the coefficient of y in the objective function is 1.5 instead of 4, the optimal decision variables remain the same: x = 51.4285 and y = 64.2857. b) It makes sense to pay $10 for an additional hour of labor. c) Suppose we have 500 pounds of extra raw material A, we can use this Excel Solver output to calculate the increase in the optimal objective value.
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illustrative_exam2_solution - Illustrative Exam 2 1...

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