A local furniture shop makes chairs, tables, sofas and lamps The projected profi

Question

A local furniture shop makes chairs, tables, sofas and lamps The projected profits 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 l-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 1-500 cubic feet of type-2 wood in stock. How many chairs and tables should the shop make in order to maximize its profit? Use table form to solve the problem Construct a computer algorithm to verify your solution.

Explanation / Answer

type -1 wood = 1000 ft, type -2 wood = 1500 ft

type 1- wood table

type 1 wood left = 1000-800-200= 0 ft, profit = 8000+2500= 10500

type2 - wood table

type 1 wood left = 1500-500-160=840 ft, profit = 3000+1600= 4600

here wood is suffecient for arrived orders, so no need to change order count, shop can produce 400 chairs 100 tables

Simple step by stem Algorithm

1. check wood type(ex: 1 or 2 or any) quantity availability (ex:1000ft)

2. initialise items count and total profit and total items produced (ex: chairs 400, total profit = 0, items produced =0), if wood is empty goto 6th step

3. check which item is more profit for less quantity of wood ( here in type -1 2 chairs needs 4ft and profit is 40 only but for 1 sofa 4 ft quantity and gets profit of 50 )

4. multiply more profit items order until wood is left and add profit to total profit, if wood is empty goto 6th step.

5.repeat 3rd step for next level profit item if wood left

6. print total items produced and total profit.

please re check your question - there should be some critical trick in question like asking orders more than suffecient wood.

type wood required order arrived total wood required profit for single item total profit items produced chairs 2 ft 400 400x2=800 ft 20 400x20=8000 400 sofa 4 ft 50 50x4=200 ft 50 50x50=2500 50

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