## Related questions with answers

Solve the given linear programming problems.

A manufacturer produces a business calculator and a graphing calculator. Each calculator is assembled in two sets of operations, where each operation is in production 8 h during each day. The average time required for a business calculator in the first operation is 3 min, and 6 min is required in the second operation. The graphing calculator averages 6 min in the first operation and 4 min in the second operation. All calculators can be sold; the profit for a business calculator is $8, and the profit for a graphing calculator is$10. How many of each type of calculator should be made each day in order to maximize profit?

Solution

VerifiedLet us assume that $x, y$ are the number of business and graphing calculators. The first process takes 3 minutes for the business calculator and 6 minutes for the graphing calculator, and we have a total of 8 hours for this process in a day, so we can write

$\begin{aligned} 3x+6y&\leq60\cdot8\\ x+2y&\leq160,&&\text{Divide both sides by 3}\\ \end{aligned}$

The second process takes 6 minutes for the business calculator and 4 minutes for the graphing calculator, and we have a total of 8 hours for this process in a day, so we can write

$\begin{aligned} 6x+4y&\leq60\cdot8\\ 3x+2y&\leq240,&&\text{Divide both sides by 2}\\ \end{aligned}$

Also, the number of calculators cannot be negative, so we have the following two inequalities:

$x\geq0,\hspace{2mm}y\geq0$

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