Answer to Question #303905 in Marketing for dagi

Question #303905

 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.


1
Expert's answer
2022-03-01T20:19:03-0500

Answer

"x" - beds, "y" - pillows

"4x+2y\\leq40\\\\\n2x+4y\\leq32\\\\\nx\\geq0\\\\\ny\\geq0\\\\\nF(x,y)=80x+55y\\mapsto max\\\\\n4x+2y=40\\\\\n\\begin{matrix}\n x & 0&10 \\\\\n y & 20&0\n\\end{matrix}\\\\\n2x+4y=32\\\\\n\\begin{matrix}\n x & 0&16 \\\\\n y & 8&0\n\\end{matrix}"



"x=8, y=4\\\\\nF=80\\cdot8+55\\cdot4=860"

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