Question Help

I'll try and get you started.

The manager buys x attackers and y defenders; you can write down how much that will cost in terms of x & y because you're given the cost of an attacker and of a defender. You also know that his maximum budget is £12M and that the cost that you've just calculated in terms of x and y must be less than that £12M. This gives you the first inequality. Can you see now how to get the second inequality?

So would one be: x+y<12m
And the second: x+3y >(or equal to) 6m

Thanks for your help!,

Not quite. Let's take the first inequality: he buys x attackers and y defenders and the total cost must be less that £12M. An attacker costs £3M, therefore x attackers must cost x times £3M. A defender costs £1M therefore y defenders costs y times £1M. The sum of these two costs must be less than £12M. You can then simplify the inequality by dividing though by a million!

The second inequality comes from the number of points required.

Okay, so that makes 3x + y < 12m ?

And do you have to relate that to points or is a whole anew iequality?

That's nearly it. Dividing out the million gives you 12 on the right hand side and also, since the manager has up to and including 12M to spend it should be 3x + y <= 12.

The points requirement gives you a second inequality that has hold simultaneously with the first.

For the second part of the question, plot the line 3x + y = 12 and the line corresponding to the second inequality and think about how the plane is divided up by these lines.

Thank you!
Just would the second one be 2y + y => 5

2x + y >= 5.

Thank you so much for all of your help!