Question

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.

Answer 1

Let

$X_1$ represent chairs and $X_2$ represent tables

$Maximize: z=2x_1 ​+10x_2\\$

Subject to;

$​2x_1 ​+5x_2 ​≤16\\6x_1 ​≤30$

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