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?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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

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