Exercise 8. A local furniture shop makes chairs, tables, sofas and lamps The pro

Question

Exercise 8. A local furniture shop makes chairs, tables, sofas and lamps The projected prots for the four products are, respectively, 20 per chair, 30 per table, 50 per sofa and 10 per lamp. The projected demand is 400 chairs, 100 tables, 50 sofas and 160 lamps. Each chair requires 2 cubic feet of type 1-wood, each sofa requires 4 cubic feet of type 1-wood, and each lamp requires 1 cubic feet of type 2- wood while, each table requires 5 cubic feet of type 2-wood. The shop has a total amount of 1,000 cubic feet of type-1 wood and 1500 cubic feet of type-2 wood in stock. How many chairs and tables should the shop make in order to maximize its prot? 1. Use table form to solve the problem 2. Construct a computer algorithm to verify your solution.

Explanation / Answer

This is a greedy programming problem.

Now, consider type-1 wood. Since, Sofa has higher prot/cf of wood ratio, it is better to make as many sofas as possible at first.

So, the shop can construct 50 sofas which will require = 50*4 = 200 cubic feet of wood.

Rest 800 cubic feet can be used to make (800/2) = 400 chairs which is exactly equal to the demand.

Now, consider type 2 wood. Since, lamp has higher prot/cf of wood ratio, it is better to make as many lamps as possible at first.

The shop can construct 160 lamps which will require = 160*1 = 160 cubic feet of wood.

Then, they can construct all 100 tables which will require = 100*5 = 500 cubic feet of wood. There would be still (1500-160-500) = 840 cubit feet wood of type 2 left.

Algorithm Pseudocode

Calculation to maximize prot Prot Wood/item Prot/cf of Wood Max Quantity/Demand Chair 20 2 cf - type 1 10 - type 1 400 Table 30 5 cf - type 2 6 - type 2 100 Sofa 50 4 cf - type 1 12.5 - type 1 50 Lamp 10 1 cf - type 2 10 - type 2 160

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