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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 700 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 4 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? 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?

Respuesta :

sqdancefan

Answer:

  • Calculus texts: 600
  • History texts: 0
  • Marketing texts: 0

Step-by-step explanation:

Each Calculus text returns $10/2 = $5 per unit of shelf space. For History and Marketing texts, the respective numbers are $4/1 = $4 per unit, and $8/4 = $2 per unit. Using 1200 units of shelf space for 600 Calculus texts returns ...

  $5/unit × 1200 units = $6000 . . . profit

Any other use of units of shelf space will reduce profit.

anthougo

The College should purchase only 600 Calculus textbooks to maximize College profits.

Data and Calculations:

Budget limit on the number of textbooks per semester = 700

Shelf space for the purchased textbooks = 1,200 units

                                                       Calculus      History      Marketing

Shelf-space occupied

by each textbook                              2                   1                  4

Profit per textbook                        $10                 $4               $8

Profit per shelf-space                    $5 ($10/2)    $4 ($4/1)     $2 ($8/4)

The highest profit per shelf space is $5 generated by Calculus.

The highest profit that the College can make over the purchase of used Calculus textbooks = $6,000 ($5 x 1,200) or ($10 x 600).

Thus, for the College to maximize its profits, it should purchase 600 Calculus textbooks, which will not exceed the textbook limit for the semester, and at the same time maximally utilize the shelf space available.

Related link: https://brainly.com/question/14293956

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