Hi Unknown. Long time. :)
Linear programming does not require calculus.
If one graphs the lines generated from the inequalities, one looks at the vertices of their intersections.
Basic linear programming may be encountered in a pre-calc course or even in college algebra. There is an entire vocation centered around linear programming and other math. It's called Operations Research.
Usually, profit is maximized. Profit = Revenue - Cost. Therefore,
Revenue = Profit + Cost.
By 'generate', do they mean that is the profit on each copy or what they are sold for?
I will assume it means profit.
Let x = # of entertainment guides and y = # of real estate guides.
We are maximizing revenue. This is the objective function.
If 'generate' means profit, then revenue would be cost + profit:
Subject to the constraints:
The cost to make is
because they only have 4000 to spare for printing.
They only have room for 18000, so another constraint is
But, they must sell at least 8000.
Assume x and y non negative
Excel Solve does a fine job of solving linear programming problems.
Are you familiar with it?
Using Excel Solver, the result says they should sell 16,000 real estate guides and no entertainment guides to max revenue.
This results in $16,000 total revenue.
Perhaps I misinterpreted the problem because 'generate' is rather ambiguous. I tried the other objective function and got a negative number of entertainment guides. So, perhaps it means profit.
EDIT:
To do this by hand though, we look at the intersections of the lines and where they cross the axes. The 'feasible region'.
There are vertices at (6250,11750), (0,8000), (0,16000), (8000,0), (16000,0)
We enter these into the objective function. The set that results in the largest number is the max revenue.
Doing so, we find that (0,16000) gives the largest max revenue.
This means 16000 restaurant guides and 0 entertainment guides should be sold to max revenue.