1. ## Graphing inequalities

Hi, hope this is in the right section.

I'm going over past IGCSE paper packs, and this one is Oct/Nov 2006 Paper 4.
If someone could please take the time to help me with this graphing problem, I'd really appreciate it. So far Ive worked out :

9a)
x + y ≤ 12
x ≥ 4

Then on b, it's easy to plot the axes, but can someone please demonstrate c and d?

2. Originally Posted by yorkey
Hi, hope this is in the right section.

I'm going over past IGCSE paper packs, and this one is Oct/Nov 2006 Paper 4.
If someone could please take the time to help me with this graphing problem, I'd really appreciate it. So far Ive worked out :

9a)
x + y ≤ 12
x ≥ 4

Then on b, it's easy to plot the axes, but can someone please demonstrate c and d?
Hi yorkey,

I did this with a TI-84+ and shaded the "wanted region" which we call the "feasible region" in linear programming.

The intersections of the three lines are at (4, 4), (4, 8) and (6, 6).

Your "profit" function would be P(x, y) = 3x + 1.5y

Substitute the points of intersection into this function to determine the greatest and least values.

3. Oh I was right with c.) then, thanks very much. :-) However with d.), I'm still struggling to get the greatest and least values. Can you explain in a bit more detail what you mean by the "profit function"?

4. Originally Posted by yorkey
Oh I was right with c.) then, thanks very much. :-) However with d.), I'm still struggling to get the greatest and least values. Can you explain in a bit more detail what you mean by the "profit function"?

Part d tells you that Tiago makes $3 for cleaning cars and$1.50 for repairing cycles.

His profit based on x cleanings and y repairs would be P(x , y) = 3x + 1.5y

Use the Profit function I defined for you.

Substitute the coordinates of the intersections into the Profit function.

Determine the greatest and least values.

For instance f(4, 4) = 3(4) + 1.5(4) = 18

Test the other two.

5. Oh yes, thanks, but how did you actually find out what the profit function is? I know how to get the answer by substituting etc.

6. Originally Posted by yorkey
Oh yes, thanks, but how did you actually find out what the profit function is? I know how to get the answer by substituting etc.

Part d says that Tiago makes a $3 profit on each car cleaning (x) and$1.50 on each cycle repair (y). Total profit = 3x + 1.50y

The intersections of the feasible region (shaded area) will yield the maximum and minimum values of the profit function.

The profit function simply states that P(x, y) = 3x + 1.5y.

P( 4, 4 ) = 18

P( 4, 8 ) = 24

P( 6 , 6 ) = 27

Ideally, Tiago would want to clean 6 cars and repair 6 cycles to maximize his profit.

7. Ah I'm sorry, I should have seen that! thanks so much for your help :-)