Show & sell can advertise its products on local radio or television(TV). The adv
ID: 3553151 • Letter: S
Question
Show & sell can advertise its products on local radio or television(TV). The advertisement budget is limited to $10,000 a month. Each minute of radio advertisement costs $15 and each minute of TV commercials costs $300. Show & sell likes to use radio advertisement at least twice as much as TV. In the menatime, it is not practical to use more than 400 minutes of radio advertisement a month. Past experience shows that TV advertisement is estimated to be 25 times more effective than that of radio.
a) Determine the optimum allocation of the budget to radio and TV advertisement.
b) Determine the worth per unit of increasing the monthly limit on radio advertisement.
c) If the monthly budget is increased to $15,000, use the unit worth measure to determine the resulting optimum measure of advertisement effectiveness.
Explanation / Answer
What you want to maximize is your advertising audience (i.e. viewers or listeners per minute of advertising).
Since it is given that TV is estimated to be 25 times as effective as radio, your objective function (z) would be:
z = x + 25y
You only missed 1 constraint, the one stating that the advertiser likes to advertise twice as much on radio as TV.
This can be expressed as:
x >= 2y, or x - 2y >= 0
So your LP formulation would be:
maximize x + 25y
subject to
15x + 300y <= 10000
x - 2y => 0
x <= 400
x,y >= 0