Finite Math for Business Question

Question

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 400 units. For each additional $5000 spent, an additional 25 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. (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) 

c) How many units does the firm sell if it spends $50,000 on advertising? (do not include any commas in your answer)

d) How much advertising money must be spent to sell 700 units? (do not include any commas in your answer)

Answer 1

y= x/200+400     as a check insert the given information of $5k spent and see if it matches.  y=5000/200+400.  y=25+400, ( the 25 from the $5k spent, and the 400 that they sell with zero spent )

 

If the firm spends $25k on advertising it will sell 525 units.  if each $5k spent generates 25 sales, then $25 k can be broken down as $5k x 5.  Each $5k generates 25 sales, so 5 times that will generate 25 x 5, or 125.  Plus the 400 units it sells without advertising, = 525 ( 125 + 400 )

 

If the firm spends $50k it will sell 650 units.  The 400 that it sells anyway, plus 10 times when it sells for spending $5k, or 250.  250+400=650

 

To sell 700 units we first subtract the 400 it sells anyway, then divide 25 into the remainder.  So we need to sell 300 units.  Each 25 units costs $5k.  300/25=12 so we will have to spend 12 x $5k or $60k.