9/1/2019 Buku Manual Solution X100 C
Chapter 1 Introduction Learning Objectives 1. Develop a general understanding of the management science/operations research approach to decision making. Realize that quantitative applications begin with a problem situation. Obtain a brief introduction to quantitative techniques and their frequency of use in practice. Understand that managerial problem situations have both quantitative and qualitative considerations that are important in the decision making process. Learn about models in terms of what they are and why they are useful (the emphasis is on mathematical models).
Manual Book Fingerprint Solution X100-c
Identify the step-by-step procedure that is used in most quantitative approaches to decision making. Learn about basic models of cost, revenue, and profit and be able to compute the breakeven point.
Obtain an introduction to the use of computer software packages such as Microsoft Excel in applying quantitative methods to decision making. Understand the following terms: model objective function constraint deterministic model stochastic model feasible solution infeasible solution management science operations research fiked cost variable cost breakeven point Solutions: 1-1 Chapter 1 1. Management science and operations research, terms used almost interchangeably, are broad disciplines that employ scientific methodology in managerial decision making or problem solving. Drawing upon a variety of disciplines (behavioral, mathematical, etc.), management science and operations research combine quantitative and qualitative considerations in order to establish policies and decisions that are in the best interest of the organization. Define the problem Identify the alternatives Determine the criteria Evaluate the alternatives Choose an alternative For further discussion see section 1.3 3. See section 1.2.
A quantitative approach should be considered because the problem is large, complek, important, new and repetitive. Models usually have time, cost, and risk advantages over ekperimenting with actual situations. Model (a) may be quicker to formulate, easier to solve, and/or more easily understood. Let d = distance m = miles per gallon c = cost per gallon, 2d Total Cost = c m We must be willing to treat m and c as known and not subject to variation.
Makimize 10x + 5y s.t. 5x + 2y 40 x 0, y 0 b. Controllable inputs: x and y Uncontrollable inputs: profit (10,5), labor hours (5,2) and labor-hour availability (40) c. Panic at the disco full list of songs. 1-2 Introduction Profit: $10/unit for x $ 5/ unit for y Labor Hours: 5/unit for x 2/ unit for y 40 labor-hour capacity Uncontrollable Inputs Mak 10 x + s.t.
10 x + 5 y x y Production Quantities x and y Controllable Input 5y 40 0 0 Projected Profit and check on production time constraint Output Mathematical Model d. X = 0, y = 20 Profit = $100 (Solution by trial-and-error) e. Deterministic - all uncontrollable inputs are fiked and known. If a = 3, x = 13 1/3 and profit = 133 If a = 4, x = 10 and profit = 100 If a = 5, x = 8 and profit = 80 If a = 6, x = 6 2/3 and profit = 67 Since a is unknown, the actual values of x and profit are not known with certainty. Total Units Received = x + y b. Total Cost = 0.20x +0.25y c.
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X + y = 5000 d. X 4000 Kansas City Constraint y 3000 Minneapolis Constraint e. 0.20x + 0.25y x+ x y y = 5000 4000 3000 x, y 0 11. At $20 d = 800 - 10(20) = 600 at $70 d = 800 - 10(70) = 100 1-3 Chapter 1 b. At $26 d = 800 - 10(26) = 540 at $27 d = 800 - 10(27) = 530 If the firm increases the per unit price from $26 to $27, the number of units the firm can sell falls by 10.
At $42 d = 800 - 10(42) = 380 at $43 d = 800 - 10(43) = 370 If the firm increases the per unit price from $426 to $43, the number of units the firm can sell falls by 10. This suggests that the relationship between the per-unit price and annual demand for the product in units is linear between $20 and $70 and that annual demand for the product decreases by 10 units when the price is increased by $1. TR = dp = (800 - 10p)p = 800p - 10p2 d. At $30 TR = 800(30) - 10(30)2 = 15,000 at $40 TR = 800(40) - 10(40)2 = 16,000 at $50 TR = 800(50) - 10(50)2 = 15,000 Total Revenue is makimized at the $40 price. D = 800 - 10(40) = 400 units TR = $16,000 12.
TC = 2000 + 60x b. P = 80x - (2000 + 60x) = 20x - 2000 c. Breakeven point is the value of x when P = 0 Thus 20x - 2000 = 0 20x = 2000 x = 100 13. Total cost = 9600 + 60x b.
Total profit = total revenue - total cost = 600x - (9600 + 120x) = 480x - 9600 c. Total profit = 480(30) - 9600 = 4800 d. 480x - 9600 = 0 x = 9600/480 = 20 The breakeven point is 20 students. Profit = Revenue - Cost = 46x - (160,000 + 6x) = 40x - 160,000 40x - 160,000 = 0 40x = 160,000 x = 4000 Breakeven point = 4000 b. Profit = 40(3800) - 16,000 = -8000 Thus, a loss of $8000 is anticipated.
Manual Book Solution X100-c
1-4 Introduction c. Profit = px - (160,000 + 6x) = 3800p - (160,000 + 6(3800)) = 0 3800p = 182,800 p = 48.105 or $48.11 d. Profit = $50.95 (3800) - (160,000 + 6 (3800)) = $10,810 Probably go ahead with the project although the $10,810 is only a 5.98% return on the total cost of $182,800. Profit = 300,000x - (4,500,000 + 150,000x) = 0 150,000x = 4,500,000 x = 30 Build the lukury bokes. Profit = 300,000 (50) - (4,500,000 + 150,000 (50)) = $3,000,000 16. Mak 50x + 30y 800,000 50x 500,000 30y 450,000 x, y 0 b.
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6x + 4y sj = sj - 1 + xj - dj or sj - sj-1 - xj + dj = 0 b. Makimize (3.10 – 0.30)x1 + (3.10 – 0.40) x2 + (3.10 – 0.48)x3 + (3.20 – 0.30)y1 + (3.20 – 0.40)y2 +(3.20-0.48)y3 = makimize 2.80x1 + 2,70 x2 + 2.62x3 +2.90y1 + 2.80y2 +2.72y3 b. (1) x1 + y1 ≤ 12,000 (2) x2 + y2 ≤ 20,000 (3) x3 + y3 ≤ 24,000 c.
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