Answer in Operations Research for Andinet #283398
2. A furniture manufacturer makes two products – tables and chairs. Processing of these products is done on two types of machines A and B. A chair requires 2 hours on machine type A and 6 hours on machine type B. A table requires 5 hours on machine type I and no time on Machine type II. There are 16 hours/day available on machine type A and 30 hours/day on machine type B. Profits gained by the manufacturer from a chair & a table are Birr 2 and Birr 10 respectively.
A. What should be the daily production of each of the two products?
B. Use graphical method of LPP to find the solution.
Let
“X_1” represent chairs and “X_2” represent tables
“Maximize: z=2x_1nnu200b+10x_2\”
Subject to;
“u200b2x_1nnu200b+5x_2nnu200bu226416\6x_1nnu200bu226430”
As represented in the graph below, the points that satisfies the constraints is given by ;
“(0,frac{16}{5}),(5,frac{6}{5})”
We input both points into the objective function, we have that “(0,frac{16}{5})”gives the the maximum value, hence no chair should be produced and approximately 4 tables should be produced
