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# Operation Management Assignment Solution

1991 words - 8 pages

OPERATIONS MANAGEMENT MGCR 472 ASSIGNMENT # 1 SOLUTION Question 1 (10 points)

a) Labor productivity: Before: After: = 7 / (3*8) = 0.292 titles per labor-hour. = 12 / (3*8) = 0.5 titles per labor-hour.

Growth = (.5 – .292) / .292 = .714 or 71.4%. b) Multifactor productivity Before: After: = 7 / (\$480 + \$300) = .008974 titles per \$ cost. = 12 / (\$480 + \$600) = .011111 titles per \$ cost.

Growth = (.011111 - .008974) / .008974 = .238 or 23.8%. c) Multifactor productivity is more appropriate because the overhead costs have changed.

d) Multifactor productivity = 14 / [(\$480 + (H*8*2)+\$400)] = .011111 titles per \$ cost. H= \$ 23.75 per hour

Question 2 (20 points) a) Sales will always ...view middle of the document...

b) Crash E by 1 week 18* 18* 13 13 15 15 Crash G by 1 week 17* 17* 12 12 14 14 Crash B by 1 week 16* 16* 12 12 14 14

Time 19* 18 14 13 16 15

Crash E by 1 week => increased cost = \$70. Crash G by 1 week => increased cost = \$75. Crash B by 1 week => increased cost = \$80. Increase = \$225. Total Cost = \$1,700 + \$225 = \$1,925. c) Perform all the crashes from part b). Then continue as follows: Crash E by 1 week 15 16* 11 12 13 14 Crash F by 1 week 15* 15* 11 11 13 13 Crash A by 1 week 14* 14* 10 10 13 13 Crash H by 1 week 13* 13* 9 9 12 12

Crash E by 1 week => increased cost = \$70. Crash F by 1 week => increased cost = \$95. Crash A by 1 week => increased cost = \$200. Crash H by 1 week => increased cost = \$300. Increase = \$665. Total Cost = \$1,700 + \$225 + \$665 = \$2,590. Earliest possible completion time is 13 weeks. d) After we perform all the crashes in part (b), we reduce the completion time to 16 weeks. If we continue and crash E and F by 1 week, we reduce the total completion time by 1 week. Cost of crashing E and F is \$70+\$95=\$165, however benefit of reducing completion time is just \$150, hence we don’t crash E and F and stop. So, the optimal project completion time is same as the one found in part (b), which is 16 weeks.

Question 4 (12 points) a) For Q ≤ 2000, (1 machine) BEP AltI = 5000/5 = 1000 (Profit function of Alt-I = 5Q – 5000) BEP AltII = 15000/10 = 1500 (Profit function of Alt-II = 10Q – 15000) For Q>2000, (2 machines) Setting profit for Alt I to zero: => (40-35)2000 + (40-30) (Q-2000) - 12000=0 => 10000 + 10Q – 20000 - 12000 = 0 => 10Q = 22000 => BEP AltI = 2200 Setting profit for Alt II to zero: => (45-25) Q - 50000=0 => 20 Q = 50000 => BEP AltII = 2500 b) For Q ≤ 2000, (1 machine) Profit function of Alt-I = 5Q – 5000 Profit function of Alt-II = 10Q – 15000 For Q>2000, (2 machines) Profit function of Alt-I = 10Q – 22000 Profit function of Alt-II = 20Q – 50000 Graphically,

If we equate the profit functions between 0 and 2000, and solve for Q, we get Q=2000. So, Alternative I is always better between 0 and 2000 (although no profit is made before 1000 units). If we equate the profit functions between 2000 and 4000, and solve for Q, we get Q=2800. Alternative I is better between 0-2800, and Alternative II between 2800-4000. So, clearly, Alternative II is always better between 2000 and 4000 units, although Alternative II does not make any money between 2000-2200 units. To summarize, For 0 < Q ≤ 2000, Alternative I with 1 machine is better; For 2000 < Q ≤ 2800, Alternative I with 2 machines is better. For 2800 < Q ≤ 4000, Alternative II with 2 machines is better. But the system will not make any profit for Q less than 1000 units or between 2000 < Q ≤ 2200.

Question 5 (20 points) a) Year 2010 2011 2012 2013 2014 2015 b) Year 2010 2011 2012 2013 2014 2015 Discount Factors 1 1.1 1.21 1.331 1.4641 1.61051 Investment 5 5...

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