math help

Question

A women clothing store makes an average $125 profit on each dress sold. $50 on each blouse. The manager target $500 a day sale.

 -what is the inequality

-graph

-maximum number needed to reach the target.

- show why axes are appropriate

Answer 1

Step 1:

(a)

The average profit on each dress is .

The average profit on each blouse is .

The manager's average profit target .

Let be the number of dresses sold.

Let be the number of blouses sold.

Now to reach manager target, sum of the total profit on dress and blouse should be greater than or equal to .

Divide each side by .

.

The inequality is .

Step 2:

(b)

The inequality is .

Express the inequality as in terms of .

The graph of the inequality   is the shaded region, where every point in the shaded region satisfies the inequality.

The graph of the equation   is the boundary of the region. Since the inequality symbol is , the boundary is drawn as a solid line to show that points on the line satisfies the inequality and the shaded region of the graph of   is the solutions to the inequality.

Here we do not consider the negative values of and , those boundary are drawn by dotted line.

Graph :

Graph the inequality .

Shade the required region.

Note :

The solid line indicates that the line satisfies the function.

The dotted line indicates that the line does not satisfies the function.

Step 3:

(d)

Observe the graph:

represents the number of dresses sold.

represents the number of blouses sold.

The values of and are always positive.

The solution is the region is where we have positive values of and .

The graph is appropriate because we do not have solutions for negative values of and .

Solution :

The inequality is .