Question

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 typeB. 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.What should be the daily production of each of the two products?Use graphical method of LPP to find the solution.

Answer 1

$\text{Let $x_1$ represent chairs and $x_2$ represent tables}\\ \text{The linear program is given by }\\ Maximize: z=2x_1+10x_2\\ 2x_1+5x_2 \leq 16\\ 6x_1 \leq 30\\ \text{As represented in the graph below, the points that satisfies the constraints is given }\\ \text{by}\\ (0,\frac{16}{5}), (5,\frac65)\\ \text{We input both points into the objective function, we have that (0,$\frac{16}{5}$) gives the }\\ \text{the maximum value, hence no chair should be produced and approximately 4 tables}\\ \text{should be produced}$