Question

. A bed mart company is in the business of manufacturing beds and pillows. The company has 40 hours for assembly and 32 hours for finishing work per day. Manufacturing of a bed requires 4 hours for assembly and 2 hours for finishing. Similarly a pillow requires 2 hours for assembly and 4 hours for finishing. Profitability analysis indicates that every bed would contribute Birr 80, while a pillow contribution is Birr 55 respectively. Find out the daily production of the company to maximise the contribution (profit). Solve the problem by graphical method.

Answer 1

$x$ - beds, $y$ - pillows

$4x+2y\leq40\\ 2x+4y\leq32\\ x\geq0\\ y\geq0\\ F(x,y)=80x+55y\mapsto max\\ 4x+2y=40\\ \begin{matrix} x & 0&10 \\ y & 20&0 \end{matrix}\\ 2x+4y=32\\ \begin{matrix} x & 0&16 \\ y & 8&0 \end{matrix}$

$x=8, y=4\\ F=80\cdot8+55\cdot4=860$