A wood products firm uses available time at the end of each week to make goods f

Question

A wood products firm uses available time at the end of each week to make goods for stock. Currently, two products on the list of items are produced for stock: a chopping board and a knife holder. Both items require three operations: cutting, gluing, and finishing. The manager of the firm has collected the following data on these products: The manager has also determined that, during each week, 56 minutes are available for cutting, 650 minutes are available for gluing, and 360 minutes are available for finishing. Determine the optimal quantities of the decision variables. Which resources are not completely used by your solution? How much of each resource is unused?

Explanation / Answer

Answer:

(a) From the above table we can see maximum profit can be earned by producing knife holder. Hence firm should produce 50 units of knife holder and generate profit of $300.

(b) Gluing times has been completely used in above solution while cutting and finishing has not been fully used.

Unused cutting = 56 minutes - 50 units * 0.8 minutes = 16 minutes

Unused finishing = 360 minutes - 50 units * 3 minutes = 210 minutes

Chopping Board Cutting Gluing Finishing (a) Minute per unit 1.4 5 12 (b) Profit per unit 2 2 2 (c ) Profit per minute (b/a)           1.43           0.40           0.17 (d) Total Minutes 56 650 360 Maximum units that can be produced
(d/a) 40 130 30 Maximum Profit can be earned ( b *30) 60

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