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A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising it sells 350 units. For each additional $3000 spent, an additional 15 units are sold.
A) If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x.
B) How many units does the firm sell if it spends $25,000 on advertising?
C) How many units does the firm sell if it spends $50,000 on advertising?
D) How much advertising money must be spent to sell 700 units?
E) Which of the following statements correctly explains the meaning of the slope?
1. If the company spends an additional $1000 on advertising, it will increases the number of units it sells by 10.
2. In order to sell one more unit, the company would need to increase the amount it spends on advertising by $100.
3. If the company spends an additional $0.01 on advertising, it will sell one more additional unit.
4. If the company increases the amount of money it spends on advertising by $300, it will double the number of units it sells.
5. None of the above.

Sagot :

Answer:

A. y = 0.005x + 350

B. 475 units

C. 600 units

D. $70,000

E. None of the above

Explanation:

A)

If the company spend $3,000 on advertisement then it can sell 15 additional units. Total the company can sell 350 units without any advertisement. Then assuming linear relationship the equation will be:

y = 15 /3000 x + 350

y = 1 / 200 x + 350

y = 0.005x + 350

B) y = 0.005 (25,000) + 350

y = 475

C) y = 0.005 (50,000) + 350

y = 600

D) $3,000 / 15 units = $200 per unit

Since 350 units are sold without any cost then additional 350 units will be sold by,

350 units * 200 $ = $70,000

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