To maximize exposure within the budget and constraints, Gauss Jordan, Inc. should buy 100 spots on The Masked Singer and 20 spots on The Conners. This satisfies all constraints including the budget and the requirement for at least 75% of the spots to be for The Masked Singer, while also using the full budget for maximum exposure.
To determine the number of spots that should be purchased on each show to maximize exposure, we will need to consider Gauss Jordan, Inc.'s constraints and calculate exposure using the formula Number of ads x Number of viewers.
Constraints
At least 120 commercial spots must be bought in total.
The budget for TV commercials is $52,000,000.
At least 75% of the total number of spots must be for The Masked Singer.
Cost per spot is $400,000 for The Masked Singer and $100,000 for The Conners.
Formulating the Problem
Let M represent the number of spots on The Masked Singer and C represent the spots on The Conners.
The constraints translate into the following equations:
M + C ≥ 120 (At least 120 spots)
400,000M + 100,000C ≤ 52,000,000 (Budget)
≥ 75% of spots must be for The Masked Singer: M ≥ 0.75(M + C)
To maximize exposure, we want to maximize the expression for exposure: (4.6M + 3.6C).
However, we need to determine the maximum number of spots we can afford under these constraints.
Since 75% of the spots must be for The Masked Singer, with a budget of $52,000,000, and each spot costs $400,000, then:
M ≥ 0.75(M + C)
M ≥ 0.75(120)
M ≥ 90
Thus, we need to buy at least 90 spots for The Masked Singer.
With the remainder of the budget, we can calculate the spots for The Conners.
Given the equation 400,000M + 100,000C ≤ 52,000,000:
We can afford M = (52,000,000 - 100,000C) / 400,000 spots of The Masked Singer.
For C, we solve C = 120 - M, since we need at least 120 spots in total.
After solving simultaneously, we find that M = 100 and C = 20 satisfies all the constraints.
Hence, to maximize exposure within the given budget and constraints, Gauss Jordan, Inc. should buy 100 spots on The Masked Singer and 20 spots on The Conners.
Question:
On Wednesday evenings in October 2021, each episode of The Masked Singer was typically watched by 4.6 million viewers, while each episode of The Conners was typically watched by 3.6 million viewers. Your marketing services firm has been hired to promote Gauss Jordan sneakers by buying at least 120 commercial spots during episodes of The Masked Singer and The Conners. You have been quoted a price of $400,000 per spot for The Masked Singer and $100,000 per spot for The Conners. Gauss Jordan, Inc.'s advertising budget for TV commercials is $52,000,000, and it would like at least 75% of the total number of spots to appear on The Masked Singer. How many spots should you purchase on each show to maximize exposure? HINT [Calculate exposure as Number of ads x Number of viewers.] (If an answer does not exist, enter DNE.)
The Masked Singer _______
The Conners ________