A political candidate wants to use a combination of radio and TV advertisements in her campaign. Research has shown that each 1-minute spot on TV reaches 0.7 million people and that each 1-minute spot on radio reaches 0.6 million. The candidate believes she must reach 66 million people, and she must buy at least 105 minutes of advertisements. How many minutes of each medium should be used if TV costs $500 per minute, radio costs $100 per minute, and the candidate wishes to minimize costs?

TV ____________min

radio ___________ min

 

TV - 0 min

Radio - 110 mins

Step-by-step explanation

For this problem, I used Microsoft Excel to calculate for the number of minutes per medium that will result to the minimum cost.

First, we should setup the calculation sheet.

Let

x = number of minutes for TV ads

y = number minutes for radio ads

Cells C2 & C3 show the number of minutes for TV and Radio ads that will yield the minimum cost.

Since we want to minimize costs, we need to set our objective function at D6 by using the corresponding costs of each medium:

f(x) = 500x + 100y

Next, in optimization problems, we should always set our constraints. In this case, I used the required number of people to be reached as a constraint. I also used the minimum number of minutes as another constraint.

• Constraint 1: 0.7x + 0.6y = 66

• Constraint 2: x + y => 105

To add these constraints to our calculation sheet, we just need to input the formula for the left-hand side of the equation as shown below. Don't mind the right-hand side for now :)

Then, we will need to setup the solver parameters.

We set the object at D6 since that is where our objective function is located. We also set it to "Min", since we want to minimize cost. In order for the objective to be met, Cells C2 & C3 or the number of minutes per medium should be changed. For the constraints, we input the right-hand side of the constraint equations as shown below. I also added an additional constraint "$C$2:$C$3=>0" to make sure that the number of minutes will be positive. Lastly, I used the Simplex Method since it is a linear problem. After all these things have been setup, you can now click solve.

Please see the attached file for the complete solution