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Dima020 [189]
1 year ago
15

John Fleming, marketing manager for the Athletic Sporting Goods Company (ASGC) is thinking about how the changes taking place am

ong retailers in his channel might impact his strategy. The ASGC is a producer of different lines of sports products. John is looking for alternative ways to make money.John Fleming is considering a new strategy to increase sales of tennis balls and new tennis racquets. a.The basic idea for ASGC is to sell tennis balls in large quantities to nonprofit groups who resell the balls to raise money. For example, a service organization at a local college bought 2,500 tennis balls printed with the college logo. The company charged $.50 each for the tennis balls-plus a $800 one-time charge for the stamp to print the logo. The service group plans to resell the tennis balls for $2.50 each and contribute the profits to a shelter for the homeless.Questions based on the above. (5 pts)5. What is the service organization's average cost per printed Tennis Ball? __________________________6. What is the total profit the service group hopes to make and contribute to the Shelter if it sells all 2500 tennis balls at $2.50 per ball?__________________
Mathematics
1 answer:
zhuklara [117]1 year ago
6 0

This problem describes a situation where a college buys 2500 tennis balls for $0.50 each plus a fee of $800 for the logo. They then sell the balls for $2.50 each. We need to determine the average cost of each tennis ball and the profit the college will have if they manage to sell all the balls at that price.

To find the average cost, we need to add the price they paid per ball plus the one-time fee, then divide by the number of balls. We have:

avg=\frac{0.5\cdot2500+800}{2500}=\frac{1250+800}{2500}=\frac{2050}{2500}=0.82

The average cost per ball is $0.82

Now we need to determine the profit, which is the subtraction between the total earnt by the cost. We have:

\begin{gathered} \text{ profit}=\text{ earnings}-\text{ cost}\\ \\ \text{ cost}=0.5\cdot2500+800=2050\\ \\ \text{ earnings}=2500\cdot2.5=6250\\ \\ \text{ profit}=6250-2050=4200 \end{gathered}

The total profit will be $4,200 if the balls are sold at $2.5

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Step-by-step explanation:

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QUESTION 1
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It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.

Let <em>θ</em> be the angle between the force vector <em>F</em> and the displacement vector <em>r</em>. The work <em>W</em> done by <em>F</em> in the direction of <em>r</em> is

<em>W</em> = <em>F</em> • <em>r</em> cos(<em>θ</em>)

The cosine of the angle between the vectors can be obtained from the dot product identity,

<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>)   ==>   cos(<em>θ</em>) = (<em>a</em> • <em>b</em>) / (||<em>a</em>|| ||<em>b</em>||)

so that

<em>W</em> = (<em>F</em> • <em>r</em>)² / (||<em>F</em>|| ||<em>r</em>||)

For instance, if <em>F</em> = 3<em>i</em> + <em>j</em> + <em>k</em> and <em>r</em> = 7<em>i</em> - 7<em>j</em> - <em>k</em> (which is my closest guess to the given vectors' components), then the work done by <em>F</em> along <em>r</em> is

<em>W</em> = ((3<em>i</em> + <em>j</em> + <em>k</em>) • (7<em>i</em> - 7<em>j</em> - <em>k</em>))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))

==>   <em>W</em> ≈ 5.12 J

(assuming <em>F</em> and <em>r</em> are measured in Newtons (N) and meters (m), respectively).

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