Answer:
Step-by-step 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
