Question

Corey Steinbruner is the marketing director for a new vitamin supplement and he wants to place ads in two magazines: Sports Illustrated and Men's Health. Corey estimates that each one-page ad in Sports Illustrated will be read by 4 million people and costs $2000 and each one-page ad in Men's Health will be read by 1 million people and costs $1000. Corey does not want to budget more than $14,000 on advertising and wants to place at least 3 ads in Sports Illustrated and at least 4 ads in Men's Health. a) Let LaTeX: xx be the number of ads in Sports Illustrated and LaTeX: yy be the number of ads in Men's Health. Write the objective function (with quantities in millions) to find the maximum number of readers reached by the ads.

Answer 1

Explanation:

From the given information:

x = number of ads in sports illustrated

y = number of ads in Man's health

Thus, the total ads read by z = (4x +y) million people

The objective function to maximize Z (millions) is:

Z = 4x + y

To determine x & y; constraint to,

x ≥ 3, y ≥ 4

Budget constraint: 2000x + 1000y ≤ 14000

By approaching the graphically

If we draw the line x = 3 , y = 4

Then;

2000x + 1000y = 14000

2x + y = 14

Corner points are A (3,4), B(5,4), C(3,8)

At A(3,4):

Z = 4(3) + 1 (4) = 16

At B(5,4):

4(5) + 1 (4) = 24

At C(3,8):

4(3) + 1(8) = 20

Thus, Z = 24 million. x = 5, y = 4

Therefore;

they should place 5 ads in sports illustrated.

4 ads in man's health to maximize the number of 24 million readers.