Question

Eco Motors manufactures alternative energy cars and pickups. The most likely customers are high-income men and women, and company managers want to initiate an advertising campaign targeting these groups. They plan to run 30-second spots on net-casts that deal with renewable energy programs, where they can reach 4 thousand woman and 12 thousands men from their target group. They also plan 30-second spots on net-casts that deal with sporting events where they can reach 3 thousand women and 12 thousand men from their target group. Eco Motors feels that the ads must reach at least 60 thousand woman and at least 216 thousand men who are prospective customers. If it cost $4,000 for each renewable spot and $6,000 for each sporting events spot. How many of each spot should be run to minimize cost? Let x = the number of renewable spots and y = the number of sporting events spots Minimum cost is at (If needed, separate points with a comma.)

a) x = 10, y = 15, Minimum cost = $130,000
b) x = 20, y = 10, Minimum cost = $140,000
c) x = 15, y = 12, Minimum cost = $132,000
d) x = 12, y = 15, Minimum cost = $124,000

Answer 1

To minimize cost, 15 renewable spots and 12 sporting events spots should be run, resulting in a minimum cost of $132,000.

Step-by-step explanation:

To minimize cost, let's set up a system of inequalities based on the number of spots that should be run. Let x be the number of renewable spots and y be the number of sporting events spots. We know that the ads must reach at least 60,000 women and at least 216,000 men. So the inequalities are:

x + 3,000 + y + 3,000 ≥ 60,000 (reaching at least 60,000 women)

4,000x + 6,000y ≥ minimum cost

12,000x + 12,000y ≥ 216,000 (reaching at least 216,000 men)

Solving these inequalities, the optimal solution is x = 15 and y = 12. Plugging these values into the cost equation, we get:

4,000(15) + 6,000(12) = 132,000

So, the minimum cost is $132,000.