Page 1 Quiz – Chapter 13-1 - Solutions 1. The term "constraints" in a linear programming model generally describes (CIA adapted) A scarce resources. B production costs. C differential costs. D dependent variables. E objective functions. Answer: A 2. Great Stride Company has a limited number of machine-hours available for products X and Y. Each product has the same selling price per unit, but X has a contribution margin of $6.00 while Y has a contribution margin of $9.00. Two units of X can be produced in the same time required for one unit of Y. How should the plant capacity be divided between the two products? There is no demand constraint on either product. A 100% to X; 0% to Y B 0% to X; 100% to Y C 57% to X; 43% to Y D 40% to X; 60% to Y Answer: A X: 2 units ($6.00) = $12.00 Y: 1 unit ($9.00) = $9.00 In a unit of time, you make $12 with X versus $9 with Y. So, you should make only XPage 2 3. The Personal Paint Company manufactures two lines of latex paint; Standard and Ultracoat. Revenues per gallon are $8 for Standard and $14 for Ultracoat. Variable costs per gallon are $4 and $6, respectively. Fixed costs are applied at the rate of $2 per gallon of Standard and $4 per gallon of Ultracoat. At least 5,000 gallons of each product must be manufactured each week. The manufacturing process requires 1 hour of machine time per gallon of Standard and 2.2 units of machine time for Ultracoat. A total of 20,000 machine-hours are available per week. How many units of each product should be manufactured per week? A 5,000 Standard, 5,000 Ultracoat B 9,000 Standard, 15,000 Ultracoat C 5,000 Standard, 15,000 Ultracoat D 9,000 Standard, 5,000 Ultracoat Answer: D The CM for one unit of each product is: Standard CM = $8 - $4 = $4 Ultracoat CM = $14 - $6 = $8 Max $4S + $8U s.t. S >= 5,000 U>= 5,000 1S + 2.2U <=20,000 S,U >= 0 Max $4S + $8U (5000, 5000) (4x5000) + (8x5000) = $60,000 (9000, 5000) (4x5000) + (8x6818) = $74,464 (5000, 6818) (4x9000) + (8x5000) = $81,000Page 3 4. The ABE Company manufactures two models of its product, C and D. Model C is processed for four hours in the machining department and two hours in the polishing department. Model D is processed for nine hours in the machining department and six hours in the polishing department. The available time for processing the two models is 200 hours per week in the machining department and 180 hours per week in the polishing department. The contribution margins expected are $10 for model C and $14 for model D. Which of the following represents the constraint for the polishing department? A 10C + 14D <= 380 B 6C + 15D < =380 C 4C + 9D < =180 D 2C + 6D < =180 Answer: D Max $10C + $14D s.t.: 4C + 9D <= 200 (machining) 2C + 6D <=180 (polishing) C,D >= 0 For questions 5-7 refer to the information below. The Etnier Company manufactures two products, S and T. There is limited production capacity available. The maximum number of units that can be produced in a month is 10,000 units. In addition to this maximum capacity, there is a limited number of machine-hours available for use in the production process. Other specific information is as follows: Product S Product T Sales price $50.00 $40.00 Variable costs $35.00 $28.00 Machine-hours required 5 2 The total machine-hours available each month is 25,000 hours. 5. What is the objective function for the Etnier Company? A Maximize: $15.00S + $12.00T = Total contribution margin B Maximize: $50.00S + $40.00T = Total revenue C Minimize: $35.00S + $28.00T = Total costs D Maximize: S + T = Total units sold Answer: A CM CMs = $50 - $35 = $15 & CMt = $40 -$28 = $12 Max $15S + $12TPage 4 6. What is the constraint for machine-hours? A 5S + 2T < =10,000 B S + T < =25,000 C 5S + 2T < =25,000 D S + T < =10,000 Answer: C 7. What is the constraint for total capacity? A S + T = 10,000 B S + T < =10,000 C 5S + 2T < =10,000 D 5S + 2T < =25,000
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