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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introductory calculus, history, and marketing texts should be purchased from students for resale. Due to budget limitations, you cannot purchase more than 1050 of these textbooks each semester. There are also shelf-space limitations: Calculus texts occupy 2 units of shelf space each, history books 1 unit each, and marketing texts 3 units each, and you can spare at most 1,900 units of shelf space for the texts. If the used book program makes a profit of $20 on each calculus text, $8 on each history text, and $16 on each marketing text, how many of each type of text should you purchase to maximize profit? HINT [See Example 3.]

calculus text(s)
history text(s)
marketing text(s)

What is the maximum profit the program can make in a semester?
$

Expert Solution

Step 1: Set up linear programming problem

Let, number of calculus texts= $x subscript 1$

number of history texts= $x subscript 2$

number of marketing texts = $x subscript 3$

So, the linear programming problem is

$M a x space Z equals space 20 space x subscript 1 plus 8 space x subscript 2 plus 16 space x subscript 3 S u b j e c t space t o space comma space space space space space space space space space space space space space space space space space space space space x subscript 1 plus x subscript 2 plus x subscript 3 less or equal than 1050 space space space space space space space space space space space space space space space space space space space 2 space x subscript 1 plus x subscript 2 plus 3 space x subscript 3 less or equal than 1900 space space space space space space space space space space space space space space space space space space space a n d space x subscript 1 comma x subscript 2 comma x subscript 3 greater or equal than 0$