Question

An educational software company produces two software packages: an algebraic solver and a graphing program. They project a demand for at least

100

algebraic solvers and

80

graphing programs each day. They can produce up to

200

algebraic solvers and

170

graphing programs per day. They need to produce at least

200

software packages each day to satisfy existing orders. Each algebraic solver makes a loss of

$ 1.50

. Each graphing program makes a profit of

$ 4 .50

. Determine how many of each software package the company should produce each way to maximize its profits.

Accepted Answer

Let $x$ be the number of algebraic solver produced and $y$ be the number of graphing program produced.

Since, they can't produce negative number of software packages. Then we have:

$200$

Also, we have:

$x \geq 100, y \geq 80$

$x \leq 200, y \leq 170$

$x + y \geq 200$

The profit relation will be the optimizing equation which is as below.

$P = - 1.50 x + 4.50 y$

So, the entire system is:

$P = - 1.50 x + 4.50 y$ subject to

$100 \leq x \leq 200$

$80 \leq y \leq 170$

$y \geq 200 - x$

Now, we will make the table at the different points of $(x, y)$ .

$(x, y)$ $P = - 1.50 x + 4.50 y$

$(100, 170)$ $615$

$(100, 100)$ $300$

$(120, 80)$ $180$

$(200, 170)$ $465$

$(200, 80)$ $60$

The feasibility region graph is as below.

We observe that maximum value of $P = 615$ is at $(x, y) = (100, 170)$ .

Hence, the company should produce $100$ algebraic solver and $170$ graphing programs.

Type of investment	Interest per annum
Municipal bond	$2 %$
Bank Mutual fund	$P = 615$
Speculative money market fund	$5 %$

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