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AE 232: Management Science First Semester 2020- PRELIMINARY EXAMINATION Name: _____AIRA M. OWAR Code: ___ Date: ____OCTOBER 8, 2020___ II. Problem Solving: Show your complete solution.
- A garment factory manufactures men’s shirts and women’s blouses. The production process includes cutting, sewing, and packaging. The factory employs 25 workers in the cutting department, 35 in the sewing department, and 5 in the packaging department. Each employee works an 8-hour shift per day for 5 days a week. The following table gives the time requirements and profit per unit for the two garments: MINUTES PER UNIT GARMENTS CUTTING SEWING PACKAGING PROFIT/UNIT SHIRTS 20 70 12 80 BLOUSES 60 60 4 120 Determine the optimal weekly production schedule for the garment factory. a. Define the variable used: (1 point)
S = Required minutes for shirts B = Required minutes for blouses Max Z = 80S+120B b. LP Model: (3 points) Maximize Z = 80S+120B Subject to: 20S + 60B ≤ 60,000 Cutting 70S + 60B ≤ 84,000 Sewing 12S + 4B ≤ 12,000 Packaging S, B ≥ 0 This study source was downloaded by 100000835799327 from CourseHero.com on 12-19-2021 02:20:42 GMT -06:
c. Identify the feasible region: (3 points) Cutting department – green Sewing department – orange Packaging department – blue CUTTING: SEWING: PACKAGING: 20S + 60B = 60,000 70S +60B = 84,000 12S + 4B = 12, 20(0) + 60B = 60,000 70(0) + 60B = 84,000 12(0) +4B = 12, 60B = 60,000 60B = 84,000 4B = 12, B = 1,000 B = 1,400 B = 3, 20S + 60B = 60,000 70S + 60B = 84,000 12S + 4B = 12, 20S = 60,000 70S = 84,000 12S = 12, S = 3,000 S = 1,200 S = 1,
(0, 1,000) (3,000, 0) > (0,1400) (1200, 0) > (0, 3000) (1000, 0) d. Corner Points and the value of the objective functions: (2 points) Corner points Value of the objective function (0,0) 80(0)+120(0)= (0, 1000) 80(0) + 120(1000) = 120, (480, 840) 80(480) + 120( 840) = 139, 200 (870, 380) 80(870)+120(380) = 115, 200 (1000, 0) 80(1,000) + 120(0) = 80,
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d. Compute total revenue (TR) function (2 points)
Total Revenue = Selling Price per Unit (SPU) = 5,000Q = 5,000(200.8) = 1,004, e. Compute the profit function (2 points) Profit = Total revenues – Total costs = 5,000Q – (502,000 + 2,500Q) = 2,500Q – 502, = 2,500(200.8) – 502, = 502,000-502, = 0 f. Find the break-even quantity (2 points) Break-even Quantity > 5,000Q = 502,000 + 2500Q 2,500Q = 502, BEQ = 502,000/2, BEQ = 200.8 UNITS g. Find the break-even sales revenue (2 points) TOTAL COST = 1,004, TOTAL REVENUE = 1,004, THEREFORE, BREAK-EVEN-SALES IS 1,004,000.
- WonderFood is a multi-product company that makes three types of cereal. Following table shows the sales price, variable cost per unit and units sold of each product: Type 1 Type 2 Type 3 Variable cost per unit $5 $7.50 $ Price per unit $10 $13 $ Unit sold 2,000 1,500 1, a. Calculate the separate contribution margin ratio for each product (6 points) TYPE 1: > Contribution Margin Ratio = (Sales Price – Variable Cost per Unit) / Sales Price This study source was downloaded by 100000835799327 from CourseHero.com on 12-19-2021 02:20:42 GMT -06:
= 0.5 or 50% TYPE 2:
Contribution Margin Ratio = (Sales Price – Variable Cost per Unit) / Sales Price = (13 – 7.50) / 13 = 5.5/ = 0.42 OR 42% TYPE 3: Contribution Margin Ratio = (Sales Price – Variable Cost per Unit) / Sales Price = (15 – 9) / 15 = 6/ = 0.4 OR 40% b. Calculate the weighted-average contribution margin ratio of the company as a whole. (8 points) Weighted Average CM Ratio = (type 1 CM ratio + type 2 CM ratio + type 3 CM ratio) / 3 = 1.32 / 3 = 0.44 or 44% c. If the company’s fixed costs are $100, 000 per annum, calculate the breakeven distribution of products. (5 points) BEQ > 38Q = 100,000 + 21.5Q 16.5Q = 100, Q = 100,000 / 16. BEQ = 6,060.61 UNITS This study source was downloaded by 100000835799327 from CourseHero.com on 12-19-2021 02:20:42 GMT -06: Powered by TCPDF (www.tcpdf.org) https://www.coursehero.com/file/100002513/AE-232-OWAR-PRELIM-PART2-SOLUTIONSdocx/
