A retail company estimates that if it spends x thousands of dollars on advertising during the year, it will realize a profit of P (x) dollars, where P (x) = - 0.5 x 2 + 120 x + 2000, where 0 ≤ x ≤ 187. a. What is the company's marginal profit at the $ 100000 and $ 140000 advertising levels? P ' (100) = P ' (140) = b. What advertising expenditure would you recommend to this company? $

Step-by-step explanation:

If the profit realized by the company is modelled by the equation

P (x) = - 0.5x² + 120x + 2000, marginal profit occurs at dP/dx = 0

dP/dx = - x+120

P' (x) = - x+120

Company's marginal profit at the $100,000 advertising level will be expressed as;

P ' (100) = - 100+120

P' (100) = 20

Marginal profit at the $100,000 advertising level is $20,000

Company's marginal profit at the $140,000 advertising level will be expressed as;

P ' (140) = - 140+120

P' (140) = - 20

Marginal profit at the $140,000 advertising level is $-20,000

Based on the marginal profit at both advertising level, I will recommend the advertising expenditure when profit between $0 and $119 is made. At any marginal profit from $120 and above, it is not advisable for the company to advertise because they will fall into a negative marginal profit which is invariably a loss.