The marketing manager for Mountain Mist soda needs to decide how many TV spots a
ID: 3783714 • Letter: T
Question
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.
Explanation / Answer
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
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