PRINTABLE VERSION Quiz 1 Question 1 Suppose you buy a piece of office equipment for $8,000. After 6 years you sell it for a scrap value of $2,000. The equipment is depreciated linearly over 6 years. The rate of depreciation of the piece of equipment is a) $1,333.33 per year b) $1,200.00 per year c) $857.14 per year d) $1,000.00 per year e) $6,000.00 per year f) None of the above. Question 2 A truck is worth $100,000.00 when purchased. It is depreciated linearly over 4 years and has a scrap value of $6,000.00. A linear equation expressing the truck's book value at the end of t years is a) b) c) d) e) f) None of the above. Question 3 Suppose you buy a piece of office equipment for $17,000.00. After 5 years you sell it for a scrap value of $5,000.00. The equipment is depreciated linearly over 5 years. The value of the piece of equipment after 4 years is (rounded to the nearest whole dollar) a) $5,000.00 b) $15,080.00 c) $14,176.00 d) $9,000.00 e) $7,400.00 f) None of the above. Question 4 A company has fixed monthly costs of $120,000 and production costs on its product of $25 per unit. The company sells its product for $56 per unit. The cost function, revenue function and profit function for this situation are a) b) c) d) e) f) None of the above. Question 5 A manufacturer has a monthly fixed cost of $70,000 and a production cost of $8 for each unit produced. The product sells for $25 per unit. If the manufacturer produces and sells 13,000 units one month, then his profit is a) $3,250,000 b) $34,000 c) $1,040,000 d) $255,000 e) $151,000 f) None of the above. Question 6 A manufacturer has a monthly fixed cost of $40,000 and a production cost of $9 for each unit produced. The product sells for $17 per unit. If the manufacturer produces and sells 8,000 units per month, indicate whether he will have a profit, loss or break-even. a) Loss b) Profit c) Break-even d) None of the above. Question 7 A manufacturer has a monthly fixed cost of $270,000 and a production cost of $60 for each unit produced. The product sells for $75 per unit. Find the break-even quantity. a) 18,000 b) 5,625 c) 1,350,000 d) 2,000 e) 3,600 f) None of the above. Question 8 A manufacturer has a monthly fixed cost of $100,000 and a production cost of $20 for each unit produced. The product sells for $31 per unit. Find the break-even revenue. a) $9,090.91 b) $3,225.81 c) $1,960.78 d) $4,761.90 e) $281,818.18 f) None of the above. Question 9 A manufacturer has a monthly fixed cost of $70,000 and a production cost of $17 for each unit produced. The product sells for $26 per unit. Find the break-even point. a) b) c) d) e) f) None of the above. Question 10 Use the feasible set shown to deterimine which corner point minimizes the objective function C = 33x + 25y. a) ( 0 , 10 ) b) (4,2) c) (0,0) d) (6,0) e) (1,6) f) None of the above. Question 11 Given the linear programming problem, use the method of corners to determine where the minimum occurs and give the minimum value. Minimize Subject to x1 y5 x+y5 x0 y0 a) ( 1 , 5 ) with C = 11 b) ( 1 , 0 ) with C = 1 c) ( 0 , 5 ) with C = 10 d) ( 0 , 0 ) with C = 0 e) ( 1 , 4 ) with C = 9 f) None of the above. Question 12 A company produces two types of bicycles; mountain bikes and racing bikes. It takes 6 hours of assembly time and 3 hours of mechanical tuning time to produce a mountain bike. It takes 10 hours of assembly time and 74 hours of mechanical tuning time to produce a racing bike. The company has at most 22 hours of mechanical tuning labor per week and at most 159 hours of assembly labor per week. The company's profit is $110 for each mountain bike produced and $150 for each racing bike produced. The company wants to make as much money as possible. Let x = the number of mountain bikes they produce, and let y = the number of racing bikes they produce. Which of the following is the objective function for the problem? a) Maximize P = 150x + 110y b) Maximize P = 16500xy c) Maximize P = 110x + 150y d) Minimize P = 150x + 110y e) Minimize P = 110x + 150y f) None of the above. Question 13 A company produces two types of bicycles; mountain bikes and racing bikes. It takes 5 hours of assembly time and 2 hours of mechanical tuning to produce a mountain bike. It takes 8 hours of assembly time and 3 hours of mechanical tuning to produce a racing bike. The company has at most 24 hours of mechanical tuning labor per week and at most 171 hours of assembly labor per week. The company's profit is $120 for each mountain bike produced and $100 for each racing bike produced. The company wants to make as much money as possible. Let x = the number of mountain bikes they produce, and let y = the number of racing bikes they produce. What are the constraints for this problem? a) 5x + 8y 171, 2x + 3y 24, x 0, y 0 b) 5x + 2y 171, 8x + 3y 24, x 0, y 0 c) 5x + 8y 171, 2x + 3y 24, x 0, y 0 d) 2x + 8y 171, 5x + 3y 24, x 0, y 0 e) 5x + 8y 171, 2x + 3y 24, x 0, y 0 f) None of the above. Question 14 A certain academic department at a local university will conduct a research project. The department will need to hire graduate research assistants and professional researchers. Each graduate research assistant will need to work 21 hours per week on fieldwork and 19 hours per week at the university's research center. Each professional researcher will need to work 13 hours per week on fieldwork and 27 hours per week at the university's research center. The minimum number of hours needed per week for fieldwork is 164 and the minimum number of hours needed per week at the research center is 131. Each research assistant will be paid $272 per week and each professional researcher will be paid $484 per week. Let x denote the number of graduate research assistants hired and let y denote the number of professional researcher hired. The department wants to minimize cost. Set up the Linear Programming Problem for this situation. a) Min C = 272x + 484y; s.t 21x + 13y 164, 27x + 19y 131, x 0, y 0 b) Min C = 272x + 484y; s.t 13x + 21y 131, 27x + 19y 164, x 0, y 0 c) Min C = 484x + 272y; s.t 21x + 19y 164, 13x + 27y 131, x 0, y 0 d) Min C = 272x + 484y; s.t 21x + 13y 164, 19x + 27y 131, x 0, y 0 e) Min C = 484x + 272y; s.t 13x + 21y 164, 27x + 19y 131, x 0, y 0 f) None of the above