Solutions to Suggested Homework Problems

Transcription

1 Solutions to Suggested Homework Problems Chapter 5. a. abor Country Output Input in Units in Hours U.S. 100,000 0, DC 0,000 15, Capital Equipment Country Output Input in Units in Hours U.S. 100,000 60, DC 0,000 5, Yes. You would expect the capital equipment productivity measure to be higher in the U.S. than in a DC. b. Multifactor abor and Capital Equipment Country Output in Units Input in Hours U.S. 100,000 0, ,000 80,000 DC 0,000 15, ,000 0, Yes, labor and equipment can be substituted for each other. Therefore, this multifactor measure is a better indicator of productivity in this instance. c. Raw Material Country Output Input in Units in Dollars U.S. 100,000 $0, DC 0,000 FC $0,000/10 $, The raw material productivity measures might be greater in the DC due to a reduced cost paid for raw materials, which is typical of DC s. Page 1 of 8

2 9. Year Output in Packages Input in Drivers , Percentage Change , ( )/ % Chapter 5 7. Current plans are to make 100 units of component A, then 100 units of component B, then 100 units of component A, then 100 units of component B, etc, where the setup and run times for each component are given below. Component Setup/Changeover Time Run Time/unit A 5 minutes 0. minutes B 10 minutes 0.1 minutes Assume the packaging of the two components is totally automated and only takes seconds per unit of the final product. This packaging time is small enough that you can ignore it. What is the average hourly output, in terms of the number of units of packaged product (which includes 1 component A and 1 component B)? (100) +.1(100) minutes/100 units 45/100 60/X X units/hr. 9. a. Take Order 100 per hour * 1 hours 100 Pick Order 80 per hour * 4 hours 190 Pack Order 60 per hour * 4 hours 1440 Maximum output is determined by order taking (100) since the pick and pack operations can work up to 4 hours to clear out their order backlog. b. If we take the maximum of 100 orders then: Pick Order 100 orders/80 per hour 15 hours Pack Order 100 orders/60 per hour 0 hours c. Orders can be taken at a rate of 100/hours and can be picked at the rate of 80/hour so they build at the rate of 0/hour. Orders are taken for 1 hours. Maximum orders waiting for picking 0/hour * 1 hours 40 d. Orders can be picked at a rate of 80/hours and can be packed at the rate of 60/hour so they build at the rate of 0/hour. Orders are picked for 15 hours. Maximum orders waiting for packing 0/hour * 15 hours 300 e. (b. revisited) If we take the maximum of 100 orders then: Pick Order 100 orders/80 per hour 15 hours Pack Order 100 orders/10 per hour 10 hours Page of 8

3 However, Packing has to wait for the orders to be picked so it would be 15 hours (c. revisited) This answer does not change. Orders can be taken at a rate of 100/hours and can be picked at the rate of 80/hour so they build at the rate of 0/hour. Orders are taken for 1 hours. Maximum orders waiting for picking 0/hour * 1 hours 40 (d. revisited) Orders can be picked at a rate of 80/hours and can be packed at the rate of 10/hour so they build at the rate of 0/hour. Orders are picked for 15 hours. Maximum orders waiting for packing 0/hour * 15 hours 0 Chapter a. b. A-B-D-E-H, also shown in the network above as the bold path. c. 15 weeks, d. C, 3 weeks; F, 1 week; and G, 1 week. 8. Page 3 of 8

4 a. A-E-G-C-D. b. 6 weeks. c. No difference in completion date. B already has slack time of and F has slack time of 1. Chapter 6 6. a. FC (P - VC) * Break-even (where FC fixed cost, P price, and VC variable cost) $300,000 ($ $8.00) * Break-even Break-even 0,000 books b. Higher c. ower 8. a. b. c. FC (P - VC) * Break-even (where FC fixed cost, P price, and VC variable cost). $900 ($ $4.50) * Break-even Break-even 900 units. FC + profit (P - VC) * V (where FC fixed cost, P price, and VC variable cost, and V Volume) $900 + $500 ($ $4.50) * V V 1400 units. Profit per unit (P-VC)*V - FC)/V $.5 (($ $4.50)*V - $900)/V.5V V V 900 V 1,00 units. Profit per unit ((P-VC)*V - FC)/V $.50 (($5.50 -$4.50)*V - $900)/V.50V V - $900.50V 900 V 1,800 units. Profit per unit ((P-VC)*V - FC)/V $1.50 (($5.50 -$4.50)*V - $900)/V 1.5V V V -900 V -1,800 units. Not possible. Page 4 of 8

5 Chapter 9A. a. UT X X T C pk min, min, min {.889,1.333}.889 3σ 3σ 3(.003) 3(.003) b. The process is capable of producing the desired quality, but at present it is not capable due to the process center. The process center should be adjusted. 6. If the process could be centered, the process capability would be UT X X T C pk min, min, min 1.111, σ 3σ 3(.003) 3(.003) Sample mean range { } 111 X 999.1, R Control limits for X-bar chart: UC, C + A R, (1.733) , X Control limits for R chart: UC D 4 R.8(1.7333) C D 3 R 0(1.7333) 0.00 Page 5 of 8

6 100 X-bar 60 Range Subgroup Mean Number Subgroup Range Number The process is in statistical control. 8. a. P S p ( 1000).06 P( 1 P). 06( 1. 06).0075 n 1000 UC P + S p.06 + (.0075).075 C P - S p.06 - (.0075).045 Subgroup P P Chart Number b. The chart indicates that the process is out of control. The administrator should investigate the quality of the patient meals. Page 6 of 8

7 Chapter 17. Cu $15 C o $50 Cu 15 P +.333, NORMSINV(.333) C + C o u Should purchase 5 + ( )(15) Super Discount should overbook 19 passengers on the flight. 8. a. DS (10000)(150) Q opt units H.0(10) R d + ss (10000/5)(4) units b. q d( T + ) + ss I (5000/5)(3+1) + 5 I 390 I 10. Q opt DS (15600)(31.) H units σ σ 4(90) 180 units From Standard normal distribution, z.05 R d + zσ 300(4) + (.05) If safety stock is reduced by 50 percent, then ss 185 units. ss zσ, ss z σ , so the service probability is 84.8% 18. Service level P.99, d 000 capsules per day, T 14 days, 5 days, σ 800 capsules per day, and I 5000 units. q d( T + ) + zσ I T + σ T + ( T + ) σ (14 + 5)(800) capsules From Standard normal distribution, z.363 q 000(14 + 5) +.363(3487.1) ,11 capsules Page 7 of 8

8 8. a. Q opt DS (0)(365)(10) H cans R d 0(14) 80 cans b. σ σ 14(6.15) 3.01 cans From Standard normal distribution, z.57 R d + zσ 0(14) + (.57) cans Order 540 cans when the on-hand inventory level reaches 339 cans. Page 8 of 8