The marketing manager for Mountain Mist soda needs to decide

The marketing manager for Mountain Mist soda needs to decide how many TV spots and magazine ads to run during the next quarter. Each TV spot costs $5,000 and is expected to increase sales by 300,000 cans. Each magazine ad costs $2,000 and is expected to increase sales by 500,000 cans. A total of $100,000 may be spent on TV and magazine ads; however, Mountain Mist wants to spend no more than $70,000 on TV spots and no more than $50,000 on magazine ads. Mountain Mist earns a profit of $0.05 on each can it sells.Find the optimal solution using MATLAB.

Solution

If you take the constraint inequalities, turn the \"<=\" into just \"=\" and solved for where those lines intersect, you get the points (10, 25), (14, 15), and so forth.

For instance, the point (X1, X2) = (10, 25), which represents buying 10 TV ads and 25 magazine ads, lies right on the boundary of satisfying 5*X1 + 2*X2 <= 100 and right on the boundary of 0*X1 + 2*X2 <= 50 (i.e., if you plug in X1 = 10 and X2 = 25 both sides of both inequalities are made to be equal).

The way to get the point (10, 25), if you didn\'t have the solution at hand, is

About step 2: notice you don\'t need to find where every line intersects every other line (unless you really like to). You don\'t need to work out where the constraint X1 >= 0 interesects the constraint 5*X1 + 2*X2 <= 100 because once you have a sense of what the graphs are, it\'s evident that those two lines intersect well outside the acceptable regions of (X1, X2) defined by the problem.

Hope that helps