2 points A company finds that there is a linear relationship

(2 points) 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 250 units. For each additional $1500 spent, an additional 15 units are sold. a) If 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 T. (do not use commas in your formula). b) How many units does the firm sell if it spends $25,000 on advertising? (do not include any commas in your answer) units c) How many units does the firm sell if it spends $50,000 on advertising? (do not include any commas in your answer) units d) How much advertising money must be spent to sell 700 units? (do not include any commas in your answer) e) Which of the following statements CORRECTLY explains the meaning of the slope? (select all as there may be more than one correct statment) A. If the company spends an additional $0.01 on advertising, it will sell one more additional unit. B. If the company spends an additional $1000 on advertising, it will increases the number of units it sells by 10 C. In order to sell one more unit, the company would need to increase the amount it spends on advertising by $100 D. If the company increases the amount of money it spends on advertising by $250, it will double the number of units it sells. E. None of the above

Solution

Let the linear relationship be y = ax + b
We know that when x=0, y= 250 ;
Hence y(0) = a*0 + b = 250;
so b=250;
Now we know that for each 1500$ extra spent on advertising, 15 additional units are sold;
Thus, dy/dx = a = change in y / change in x = 15/1500 = 1/100;
Thus, a=1/100;
Thus y = x/100 + 250;

b) if 25,000 $ are spent on advertisign then y = 25000/100 + 250 = 250+250 = 500 units

c) if 50000$ are spent on advertising then y = 50000/100 + 250= 500+250 = 750 units  

d) To sell 700 units, y=700 ;
x/100 + 250 = 700;
x/100 = 700-250 = 450;
x= 450*100 = 45000
Thus, to sell 700 units, a total of 45000 $ are to be spent on advertising

e) choices B and C are correct as, to sell one more unit; you would need dx/dy additional spending, which is = 100;
Also, if it increases its advertising spedning by 1000$ then it will be able to sell 1000/100 = 10 units additionally;