Answered: TOPIC: Linear programming One company…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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TOPIC: Linear programming

One company makes and sells two different models of tools Hammers and shovels. Its manufacture requires a manual work of 20 minutes for the hammers and 30 minutes for the shovels; and a machine work of 10 minutes for hammers and 10 minutes for shovels. 100 hours per month are available for manual work and 80 hours per month for the machine. Knowing that the profit per unit is 30 and 80 pesos for hammers and shovels, respectively, plan the production to obtain the maximum profit.

Expert Solution

Step 1

make a table for the given data.

	Hammer	Shovel	Maximum Availability
Time (in minutes) required for manual work	20	30	100
Time (in minutes) required for machine work	10	10	80
Profit per unit	30	80

Let there are x units of hammers and y units of shovel.

The objective function $M a x i m i z e z = 30 x + 80 y$

subject to constraints

$20 x + 30 y \leq 100 10 x + 10 y \leq 80$

the non negative constraints are $x \geq 0, y \geq 0$

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