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 750 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 1,200 units of shelf space for the texts. If the used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, how many of each type of text should you purchase to maximize profit?

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

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

Answer 1

Explanation:

Maximum textbook to purchase is 750books

Calculus texts occupy 2 units of shelf space each,

history books 1 unit each,

marketing texts 3 units each.

Profit on calculus is $10

Profit on history $4

Profit on Marketing $8

Let calculus be x

Let marketing be y

History be z

Maximum textbooks is 750

x+y+z = 750. Equation 1

Total units =1200.

2unit calculus + 3unit marketing and 1 unit History =1200

2x + 3y +z = 1200. Equation 2

Calculus has the highest value, so to maximize profit, all the calculus books must be bought.

So since their are 1200 units of self space and calculus uses 2units

Then total unit ratio is 2+3+1=6

Then, available space for calculus is

Calculus = 2/6×1200 =400books

So all the calculus book must be bought

So, x=400

To maximum profit again we must buy again more of Marketing

Then, marketing occupy 3units

Then, available space for marketing is

Marketing. =3/6 ×1200 = 600books

So since the maximum book to buy for a semester is 750 books

Then, since we must buy only 750books and 400books already calculus, so we still have ability to buy 600books from marketing to maximize profit, but we only have 350books left to buy, then the 350books of marketing will be bought

So, no book from history will be bought to maximize profit

So

Calculus is 400books

Marketing is 350books

History is 0 books

2. Maximum profit is given by the amount of book bought multiply by it's selling price.

Maximum profit =400×10 + 350×8 +0×4

Maximum Profit = 4000+2800+0

Maximum profit = $6800

The maximum profit the program can make in a semester is $6800