Answer to Question #283116 in Discrete Mathematics for WMAJ

Question

A school organized a book fair and in this book fair a book seller is selling his books under the following rules:

There are three different packages available.

First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. The book fair has a total of 250 Islamic books, 300 Science books, and 270 Geography books. First package makes a profit of Rs. 120, second package makes Rs.100 and third package makes Rs.270 per pack. 

How many packs should be made to maximize book fair profits?

What will the profit be?

Answer 1

This is a linear programming problem that requires three elements and three constraints.

$X_1=Package1$

$X_2=Package2$

$X_3=Package 3$

Objective Function:

$Max Z =120X_1+100X_2+270X_3$

Subject to:

$2X_1+2X_2+3X_3=250$

$2X_1+4X_2+4X_3=300$

$2X_1+1X_2+5X_3=270$

$X_1,X_2,X_3>0$

$X_1=82$

$X_2=16$

$X_3=18$

$Max Z =(120\times82)+(100\times16)+(270\times18)=16300$