Question

A cabinet shop produces and installs cabinets. Business is good, and the shop has an unlimited number of customers willing to pay $100 for each cabinet in- stalled. However, for the next month, the shop has only 1750 hr of labor and 1032 units of wood that it can commit for cabinet production. Each installed cabinet requires 5 hr of labor, 3 units of wood, and one frame. The frames can be prepared in the shop before installation, with each frame requiring 2 hr of the shop's labor and 1 unit of its wood, or they can be bought ready for instal- lation from the local mill for $27 each. The shop pays $6/hr for labor, $5/unit for wood, and only pays for the labor and wood used. For the next month, how many cabinets should the shop install, and how should the necessary frames be generated so that net income is maximized?

Answer 1

Answer:

He should install 344 cabinets and the frames should be bought for installation from the local mill

Explanation:

Time available for labor = 1750 hr, number of woods available = 1032 units

Requirement for each cabinet installed

5 hr labor, 3 units of wood and 1 frame

Number of cabinets that can be produced is 344

Total expenditure for 344 installed cabinets = (1720 hr of labor×$6) + (1032 units of wood × $5) + (344 frames × $27) = $10,320+$5,160+$9,288 = $24,768

Revenue = 344 × $100 = $34,400

Net income = $34,000 - $24,768 = $9,632