Answer to Question #328016 in Operations Research for Busi

Question

A self-service photo centre allows you to make prints of pictures on an A4 size page. Two types of layouts

are available:

nnnnnlayout x: four pictures are fitted on one page, each has size 6 cm by 4 cm

nnnnnlayout y: two pictures are fitted on one page, each has size 15 cm by 9 cm

It costs R30 to print one page with layout x and it costs R40 to print one page with layout y.

You want at least 16 pictures of any size, and you are willing to spend up to R240. Write and graph a

system of inequalities that models the situation. Shade the solution space of the system of inequalities.

Answer 1

Let x be the number of pages in layout x and y - number of pages in layout y.

Layout x has 4 pictures on one page, layout y has 2 pictures on one page and we want at least 16 pictures of any size. So the first inequality looks like:

4x + 2y ≥ 16

It costs R30 to print one page with layout x and it costs R40 to print one page with layout y and we are willing to spend up to $240. So the second inequality looks like:

30x + 40y ≤ 240

Our system of inequalities is:

$\begin{cases} 4x + 2y ≥ 16 \\ 30x + 40y ≤ 240 \end{cases}$

We also should remember that x and y are numbers of pages so they can only be nonnegative.

Let's graph this system.

Blue and red line and shade is the solution of the first and second inequalities respectively.

Green shaded triangle is the solution space of the system of inequalities.