Final answer:
To maximize the number of ad exposures, we need to set up constraints for the number of newspaper and radio ads based on their costs and frequency. We also need to consider the budget constraint. The objective is to optimize the number of ad exposures based on their reach to potential customers.
Step-by-step explanation:
To maximize the number of ad exposures to potential customers, we need to determine the number of newspaper ads (n) and radio ads (r) that can be placed within the given budget constraints.
Let's start by setting up the constraints:
- Newspaper ads cost $240 each and can't run more than 23 times per month. So, the constraint for newspaper ads is: n <= 23
- Radio ads cost $500 each and can't run more than 35 times per month. So, the constraint for radio ads is: r <= 35
Next, we need to consider the budget constraint. The company has $13,350 available per month for advertising. So, the total cost of newspaper ads (240n) and radio ads (500r) should be less than or equal to $13,350:
Now, let's consider the reach or potential customers of each type of ad. Each newspaper ad reaches 6100 potential customers and each radio ad reaches 7200 potential customers. So, the total number of exposures can be calculated as: 6100n + 7200r.
To maximize the number of ad exposures, we need to optimize the objective function 6100n + 7200r, subject to the constraints mentioned above.
Solving this optimization problem will provide the optimal values for n and r, giving us the maximum number of ad exposures within the given budget.