Company's Estimated Profits

[nycmathguy]

Section 2 3
90 (a-b)

Seeking a hint only for parts (a) and (b).

 

[MathLover1]

The graph below shows a company's estimated profits for different advertising expenses. The company's actual profit was $936,660 for an advertising expense of $300,000
(a) From the graph, it appears that the company could have obtained the same profit for a lesser advertising expense. Use the graph to estimate this expense.


the graph shows the point
(30, 936,660)

estimated same profit for less is around 20

so, other point is (20, 936,660)
(you get it drawing a line segment parallel to x-axis from the point (30, 936,660)


(b) The company's model is

P=-140.75x^3+5348.3x^2-76560
0<=x<=35

substitute estimate x=20 from part a
P=-140.75*20^3+5348.3*20^2-76560
P=-1126000+2139320-76560
P=936760-> it's very close to 936660, means estimate of 20 should be little bit less

check real solution
-140.75x^3+5348.3x^2-76560=936660.....calculating we get

a solution:
x≈19.9978 -> which is very close to x=20
x≈30

 

[nycmathguy]

The graph below shows a company's estimated profits for different advertising expenses. The company's actual profit was $936,660 for an advertising expense of $300,000
(a) From the graph, it appears that the company could have obtained the same profit for a lesser advertising expense. Use the graph to estimate this expense.


the graph shows the point
(30, 936,660)

estimated same profit for less is around 20

so, other point is (20, 936,660)
(you get it drawing a line segment parallel to x-axis from the point (30, 936,660)


(b) The company's model is

P=-140.75x^3+5348.3x^2-76560
0<=x<=35

substitute estimate x=20 from part a
P=-140.75*20^3+5348.3*20^2-76560
P=-1126000+2139320-76560
P=936760-> it's very close to 936660, means estimate of 20 should be little bit less

check real solution
-140.75x^3+5348.3x^2-76560=936660.....calculating we get

a solution:
x≈19.9978 -> which is very close to x=20
x≈30

I thank you wholeheartedly for solving the problem in full but I requested hints for me to do on my own.