Question

Beach cruises prints brochures and fliers to advertise their dolphin watching tours. To print, the brochure requires three pages while the flier requires two. They are limited to 500 sheets of paper, but need to print at least 80 brochures and 100 fliers. Each brochure cost .10 to print and each flier costs .06 to print. How many of each should their print to minimize their cost?

Answer 1

Let x the number of brochures and y the number of fliers.

Optimizing function⇒ f(x,y) = 0.1 x + 0.06 y

Constraints:

x ≥ 80

y ≥ 100

3x + 2y ≤ 500

See the attached figure which represents the constraints.

From the attached figure:

The vertices of the feasible region are (80, 100), (80, 130) and (100, 100).

Substitute the points (80, 100), (80, 130) and (100, 100). in the function

f(x,y) = 0.1 x + 0.06 y

If (x,y) = (80, 100) ⇒ f(x,y) = 14

If (x,y) = (80, 130) ⇒ f(x,y) = 15.8

If (x,y) = (100, 100) ⇒ f(x,y) = 16

The minimum value 14 at (80, 100).

To minimize the cost, she would print 80 brochures and 100 fliers.