Question

Each year, thousands of people visit Yellowstone national park. Audiotapes for visitors include interviews with early settlers and information about geology, wildlife, and activities of the park. The revenue r(x) from the sale of x tapes is r(x)=9.5x. Suppose that the function for the cost of manufacturing x tapes is c(x)=0.8x+1940.
What function could be used to find the profit on x tapes?
a. Write the profit function.

b.find the profit on 500, 1000, and 5000 tapes.

c. Check by finding the revenue and the cost for each number of tapes and subtracting to find profit

Answer 1

Answer: p(x) = 8.7x - 1940

              p(500) = $2410

              p(1000) = $6760

              p(5000) = $41,560

Step-by-step explanation:

p(x) = r(x) - c(x)

      = 9.5x - (0.8x + 1940)

      = 9.5x - 0.8x - 1940

      = 8.7x - 1940

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p(500) = 8.7(500) - 1940

           = 4350 - 1940

           = 2410

p(1000) = 8.7(1000) - 1940

             = 8700 - 1940

             = 6760

p(5000) = 8.7(5000) - 1940

              = 43,500 - 1940

              = 41,560

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p(500) =    r(500)    -    c(500)

           = 9.5(500)  -  [0.8(500) + 1940]

           =    4750     - (400 + 1940)

           =     4750    -      2340

           =              2410

p(1000) =   r(1000)    -    c(1000)

            = 9.5(1000)  -  [0.8(1000) + 1940]

            =     9500     - (800 + 1940)

            =     9500     -      2740

            =              6760

p(5000) =    r(5000)    -    c(5000)

           = 9.5(5000)  -  [0.8(5000) + 1940]

           =    47500     - (4000 + 1940)

           =    47500     -      5940

           =              41,560