Answer in Operations Research for Dereje #283697

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.

“text{Let $x_1$ represent chairs and $x_2$ represent tables}\ntext{The linear program is given by }\nMaximize: z=2x_1+10x_2\n2x_1+5x_2 leq 16\n6x_1 leq 30\ntext{As represented in the graph below, the points that satisfies the constraints is given }\ntext{by}\n(0,frac{16}{5}), (5,frac65)\ntext{We input both points into the objective function, we have that (0,$frac{16}{5}$) gives the }\ntext{the maximum value, hence no chair should be produced and approximately 4 tables}\ntext{should be produced}”