+0

# Word Problems

0
404
4
+771

Jack was named manager of the month at Sylvania Wire Company due to his hiring study. The study showed that each of the 30 salespersons he supervised averaged \$50,000 in sales each month, and that for each additional salesperson he would hire, the average sales would decrease by \$1,000 per salesperson.

a) Write a function for Jack's study showing the total sales as a function of the number of additional salesperson Jack hires.

b) Use your function to determine how many salespersons Jack should hire to maximize the income from sales. What is the maximum sales Jack's company can anticipate according to the model?

Oct 24, 2017

#1
+98125
+1

These are always a little difficult for me to think of the correct function!!!

a. Call x the number  of additional people hired ........  so we have

Sales =  (30 + x) (50000 - 1000x)  =   -1000x^2 + 20000x + 1500000

b. To find the number of additional hires that will maximize revenue......we can use

x =  -20000 / [ -2 * 1000]  =  -20000 / -2000  =  10 additional people hired will maximize the revenue

The max sales  will be   (30 + 10) (50000 - 1000 (10) )  =  40 * 40000  = \$ 1,600,000

Oct 24, 2017
#2
+771
+1

Where did you get x =  -20000 / [ -2 * 1000]?

#3
+98125
+1

Sorry.....I should have explained that....!!!!

In a quadratic that has the form  ax^2 + bx + c, the  maximum  [ or minimum]  is produced at the x value  given by :

-b  / [  2a]

So  ......using our function    -1000x^2 + 20000x + 1500000

a =  -1000      and b  =  20000

So....the x value [ additional employees hired ]  that produces the max revenue  is

-20000 / [ 2 ( -10000) ]  =    -20000 / -2000  = 10

Does that help ???

Oct 24, 2017
edited by CPhill  Oct 24, 2017
#4
+771
+1

Yes! Thanks so much CPhill!