Answer to Question #249523 in Management for pat

Question

1. The JAV Company manufactures two types of lamps; Special lamp and regular lamp. Each special lamp requires 4 pounds of brass and each regular lamp requires 8 pounds of brass. During each production period, the company's brass supply limited to 640 pounds. Each special lamp requires 6 hours of milling time in the machines and each regular lamp requires 2 hours of milling time in the machine, The company's machine are available only for 360 hours in each production period. Each special lamp requires 5 light bulbs that must be imported from Hongkong. The importation of these bulb is limited to 200 units. The contribution to profit of each special lamp and regular lamp are P400 and P360 respectively. How many units of the special lamp and regular lamp should be produced per production period in order to maximize the profit?

Answer 1

Finding out how many units of the special and normal lamps were made maximizes profit. Below are the equations and calculations.

 This is a linear programming problem.

First, define variables and let x be number of special lamps,

Y to be number of regular lamps.

Therefore,

x= special lamps

Y=regular lamps

Second, state objective function i.e

M = 400x + 360y

Third,

Next constraints i.e

x,y>=0

4x+8y<=640

6x+2y<=360

Find x<=200/5

Fourth,

Find points by algebra and substitute into the equation M = 400x + 360y 

The points are (0,0), (40,60), (40,0), (0,80) and by substituting we get:

(0, 0) = $0 

(0, 80) = $28,000

(40, 60) = $37,000 

(40, 0) = $16,000