c) Suppose a local equipment rental company is willing to rent you additional ma

Question

c) Suppose a local equipment rental company is willing to rent you additional ma chine time on an hourly basis How much would you be willing to pay per hour for additional lathe and grinding machine work? (d) Suppose that the profit per 100 units of elbows fell to $500. How would this changs your production policy, and what would be your new optimal daily operating profic? to mandatory rest periods (e) Suppose the local labor union demanded an extension t each shift, which would reduce your available work time to 21 person day. How would this affect your production policy and daily profit margin? hours per 4.18. A poultry farmer owns 100 laying hens. Each week a hen can either lay 12 eggs or hatch 4 eggs, but not both. At the end of the four-week period all eggs and chicks will be sold; an egg will bring 10 cents and a chick will bring 60 cents Assume that an egg can be hatched only in the week after it is laid. Otherwise it must be saved and sold for 10 cents. Also, assume that there are no eggs available for hatching in the first weck Formulate a linear program that will suggest a hen-management strategy that will maximize profit for this operation. 4.19. You are the production manager for a very large construction company that is about to start a major concrete pour that is estimated to last for 10 days Your primary job dur- ing this time is to provide the necessary forms each day Day | 60 | 80 | 70 | 50 | 60 | 90 | 80 | 50 | 100 Forms needed 50

Explanation / Answer

Laying 12 eggs will fetch the farmer 1.20 $ ( 12 * 10 cents) and hatching 4 will fetch the farmer ( 4 * 60 cents ) = 2.40$

Hence, the best strategy would be to make all hens hatch eggs. However, there won't be any eggs to hatch if they hens do not lay them.

So, we must try to allocate the hens such that the number of eggs laid in a week are same as the number of eggs hatched.

Since, the speed of hatching and laying are in the ratio 1 : 3 ( 4 eggs hatched for every 12 eggs laid) , the allocation for hens should be done in the ratio 3 : 1

Thus, out of 100 hens, 75 hens should hatch eggs and 25 hens should lay eggs, giving us

25 * 12 = 75 * 4 = 300 chicks every week.

Thus, at the end all the eggs would be hatched and everything can be sold for 60 cents a piece. This will thus maximise the profit.

Hope this explains well.

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