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Sidana [21]
3 years ago
12

You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introdu

ctory 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?
Mathematics
1 answer:
mariarad [96]3 years ago
7 0

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.

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3 years ago
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Wittaler [7]

Answer:

We are 95% confident that the percent of executives who prefer trucks is between 19.43% and 33.06%

Step-by-step explanation:

We are given that in a group of randomly selected adults, 160 identified themselves as executives.

n = 160

Also we are given that 42 of executives preferred trucks.

So the proportion of executives who prefer trucks is given by

p = 42/160

p = 0.2625

We are asked to find the 95% confidence interval for the percent of executives who prefer trucks.

We can use normal distribution for this problem if the following conditions are satisfied.

n×p ≥ 10

160×0.2625 ≥ 10

42 ≥ 10 (satisfied)

n×(1 - p) ≥ 10

160×(1 - 0.2625) ≥ 10

118 ≥ 10 (satisfied)

The required confidence interval is given by

$ p \pm z\times \sqrt{\frac{p(1-p)}{n} } $

Where p is the proportion of executives who prefer trucks, n is the number of executives and z is the z-score corresponding to the confidence level of 95%.

Form the z-table, the z-score corresponding to the confidence level of 95% is 1.96

$ p \pm z\times \sqrt{\frac{p(1-p)}{n} } $

$ 0.2625 \pm 1.96\times \sqrt{\frac{0.2625(1-0.2625)}{160} } $

$ 0.2625 \pm 1.96\times 0.03478 $

$ 0.2625 \pm 0.06816 $

0.2625 - 0.06816, \: 0.2625 + 0.06816

(0.1943, \: 0.3306)

(19.43\%, \: 33.06\%)

Therefore, we are 95% confident that the percent of executives who prefer trucks is between 19.43% and 33.06%

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3 years ago
What is the slope of the line through (-7,-8)(−7,−8)left parenthesis, minus, 7, comma, minus, 8, right parenthesis and (0,4)(0,4
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Answer:

12/7

Step-by-step explanation:

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