LINEAR PROGRAMMING QUESTION

Question

Paperback book cost $15 each and hardcover books cost $21 each. A library has $315 to spend on books. Find the maximum number of books that the library could buy.

Answer 1

Let p = the number of paperback books.

Let h = the number of hardcover books.

The total number of books = p + h

The total value of all the books: $315 = $15(p) + $21(h)

Finding the intercepts by plugging in zero for each value:

1. When h = 0, p= 21
2. When p = 0, h = 15

Making a table of values for all whole number values from 0 - 15 for h results on whole number ordered pairs

(h, p) of (0, 21), (5, 14), (10, 7), and (15, 0).

Thus, the maximum number of books that can be purchased is 21 paperback books.

To see this visually, graph 315 = 15p + 21h with p as the horizontal axis and h as the vertical axis.