Answer to Question #281079 in Operations Research for Fikre B

Question

1)   3F manufacturer produces two products: Beds and Chairs. Each unit of Bed requires 3 hrs in molding unit, 4hrs in painting unit, and 1 hr in finishing. On the other hand, each unit of Chair requires 3 hrs in molding unit, 2 hrs in the paint shop and 2 hours in finishing. Each week, there are 210 hrs available in molding, 200hrs in painting, and 120 hrs in finishing unit. The demand for Beds cannot exceed 40 units per week. Each unit of Bed contributes Birr 20 to profit, while each unit of chair contributes Birr 30. Determine the number of units of each product per week to maximize the profit?

Answer 1

$max\ z=20x+30y$ , profit

$3x+3y\le 210$ , molding time

$4x+2y\le 200$ , painting time

$x+2y\le 120$ , finishing time

$x\le 40$ , demand for Beds

x is units of beds,

y is units of chairs

Objective function value at extreme points:

$z(40,0)=800$

$z(40,20)=1400$

$z(30,40)=1800$

$z(20,50)=1900$

$z(0,60)=1800$

The maximum value of the objective function Z=1900 occurs at the extreme point (20,50).

$x=20,y=50$