The Thompson Company manufactures two industrial products, standard ($45 profit per item) and economy ($30 profit per item). These items are built using machine time and manual labor. The standard product requires 2 hr of machine time and 1 hr of manual labor. The economy model requires 2 hr of machine time and no manual labor. If the week's supply of manual labor is limited to 900 hr and machine time to 9,000 hr, how much of each type of product should be produced each week to maximize the profit?

Question

The Thompson Company manufactures two industrial products, standard ($45 profit per item) and economy ($30 profit per item). These items are built using machine time and manual labor. The standard product requires 2 hr of machine time and 1 hr of manual labor. The economy model requires 2 hr of machine time and no manual labor. If the week's supply of manual labor is limited to 900 hr and machine time to 9,000 hr, how much of each type of product should be produced each week to maximize the profit? ​

Quizplus · Accepted Answer

To maximize profit, we need to use the constraints provided effectively. The constraints are 900 hours of manual labor and 9,000 hours of machine time. The standard model requires 2 hours of machine time and 1 hour of manual labor, while the economy model requires 2 hours of machine time and no manual labor. Let's denote the number of standard models produced as S and the number of economy models produced as E. The constraints can be written as:- For machine time: 2S + 2E ≤ 9,000- For manual labor: S ≤ 900To maximize profit, we aim to use as much of the limited resources (machine time and manual labor) as possible while adhering to the constraints. Producing 900 standard models uses 900 hours of manual labor (fully utilizing the manual labor constraint) and 1,800 hours of machine time. This leaves 7,200 hours of machine time, which can be used to produce economy models. Since each economy model requires 2 hours of machine time, 7,200 hours allows for 3,600 economy models to be produced.Thus, producing 900 standard models and 3,600 economy models uses the available resources most efficiently while adhering to the constraints, likely maximizing profit.

The Thompson Company Manufactures Two Industrial Products, Standard ($45 Profit