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 1,100 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 What is the maximum profit the program can make in a semester ?
A)you should purchase 600 history texts, no calculus texts and no marketing texts. The maximum profit is $6,000 per semester
B) you should purchase 600 calculus texts, 700 history texts and no marketing texts. The maximum profit is $6,000 per semester
C) you should purchase 700 calculus texts, 600 marketing texts and no history texts. The maximum profit is $6,000 per semester
D) you should purchase 600 calculus texts, no history texts and no marketing texts. The maximum profit is $6,000 per semester
E) you should purchase 600 marketing texts, no calculus texts and no history texts. The maximum profit is $6,000 per semester

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 1,100 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  What is the maximum profit the program can make in a semester  ?
A)you should purchase 600 history texts, no calculus texts and no marketing texts. The maximum profit is $6,000 per semester
B) you should purchase 600 calculus texts, 700 history texts and no marketing texts. The maximum profit is $6,000 per semester
C) you should purchase 700 calculus texts, 600 marketing texts and no history texts. The maximum profit is $6,000 per semester
D) you should purchase 600 calculus texts, no history texts and no marketing texts. The maximum profit is $6,000 per semester
E) you should purchase 600 marketing texts, no calculus texts and no history texts. The maximum profit is $6,000 per semester

Quizplus · Accepted Answer

Let x be the number of calculus texts, y be the number of history texts, and z be the number of marketing texts. 
We want to maximize profit, which is given by 10x + 4y + 8z. 
We also have the following two constraints: 
- x + y + z ≤ 1100 (due to budget limitations) 
- 2x + y + 3z ≤ 1200 (due to shelf-space limitations)

We can graph these constraints and shade the feasible region.

The corner points of the feasible region are: 
- (0, 0, 400) 
- (0, 600, 200) 
- (550, 250, 100) 
- (1100, 0, 0)

We can now evaluate profit at each of these points: 
- (0, 0, 400): profit = 3200 
- (0, 600, 200): profit = 3200 
- (550, 250, 100): profit = 6600 
- (1100, 0, 0): profit = 11000

The maximum profit is achieved at (550, 250, 100), which means we should purchase 550 calculus texts, 250 history texts, and 100 marketing texts. The maximum profit is $6,600 per semester.

You Are in Charge of Purchases at the Student-Run Used-Book