Question

The annual cost C (in thousands of dollars) and revenue R (in thousands of dollars) for a company each year from 2010 through 2016 can be approximated by the models C 254-9r1.1 and R343+3.4t where t is the year, with t 10 corresponding to 2010. (a) Write a function P that represents the annual profit of the company P) (b) Use a graphing utility to graph C. R, and P in the same viewing window ft) ft) 400 400 300 300 200 200 100 100 11 12 14 15 16 11 12 13 14 15 ft) 400 400- 300 300 200 200 10 1 100 Type here to search M3. Assignment: Larson4e Ocean connect op conmiuiny coege in https//www.webassign.net/web/Student/Assignment-Responses/last7dep 21262985 Pt) (b) Use a graphing utility to graph C, R, and P in the same viewing window f(t) f(t) 400 400 300 300 200 200 100 100 11 12 13 14 15 16 11 12 13 14 15 16 ft) ft) 400 400 300 300 200 C 200 100 100 11 12 13 14 15 16 11 Need Help? 12 13 14 15 Read it 16 Your wo in questons) 1 will also be submted or saved Type here to search

Answer 1

C = 254 - 9t + 1.1t²

R = 343 + 3.4t

a) Profit = Revenue - Cost

=> P = R - C

=> P = 343 + 3.4t - 254 + 9t - 1.1t²

=> P = - 1.1t² + 12.4t + 89

Therefore,

P(t) = - 1.1t² + 12.4t + 89

b) The graph is as below:

  

400- 300- 200- T00 12 15 10 11 13 14 16 CO

The blue curve represents Revenue

The red curve represents cost

The violet color represents Profit

Option B is the correct graph