Thread: Inequalities help...

This question has to be solved using inequalities with the means of a graph. But despite breaking my head on it several times, I am unable to reach a viable solution.

"A supermarket sells two kinds of washing powder, Sure-clean and Quick-Wash. At least three times as much Sure-Clean is sold as Quick-wash. The supermarket has, at most, 1800cm^2 of shelf space for washing powders. A box of Sure-Clean requires 25cm^2 of shelf space, whilst a box of Quick-wash requires 15cm^2. The profit per box is 8p for Sure-Clean and 12p for Quick-Wash. How many boxes of each kind of powder should be stocked for maximum profit? What is the maximum profit?"

Please help me setup the inequality. I can handle the graphing and finding the solution for the inequality.

Thank you

Hello, struck!

A supermarket sells two kinds of washing powder, Sure-Clean and Quick-Wash.
At least three times as much Sure-Clean is sold as Quick-Wash.
The supermarket has, at most, 1800cm² of shelf space for washing powders.
A box of Sure-Clean needs 25cm² of shelf space; a box of Quick-wash needs 15cm².
The profit per box is 8p for Sure-Clean and 12p for Quick-Wash.
How many boxes of each kind of powder should be stocked for maximum profit?
What is the maximum profit?

We have: .

We are also told that: .

And we have: .


. . Go for it!

Thanks a lot for that.. but I am not able to graph it ...

More help please..

Hello, struck!


We assume: .

We have: .


[1] and [2] places us in Quadrant 1.

Graph the line of [3]: .
It has intercepts (72,0) and (0,120).
Graph the line and shade the region below it.

Graph the line of [4]: .
It contains the origin and has slope 1/3.
Graph the line and shade the region below it.

Your graph should look like this:

Code:

        |
 (0,120)*
        | *
        |   *
        |     *
        |       *           *
        |         *     *
        |           o
        |       *:::::*
        |   *:::::::::::*
      - o - - - - - - - - o - -
        |              (72,0)

Can you finish it now?