Question 696081: The price P (in dollars) that a radio manufacturer is able to charge for a radio is given by P =40-4x^2 where x is the number (in millions) produced. It costs the company $15 to make a radio.
a.) Write an expression for the company's total revenue in terms of x (Could you explain the process for finding this expression?)
b.) Write a function for the company's profit P by subtracting the total cost to make x radios from the expressions in Part A(the one just found)
c.) Currently, the company produces 1.5 million raidos and makes a profit of $24,000,000. Write and solve an equation to find a lesser number of radios that the company could sell and still make a profit.
d.) Do all the solutions in part c make sense in this situation? Explain.
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Sorry for the long word problem, but I would appreciate it if someone responds
Thank You
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The price P (in dollars) that a radio manufacturer is able to charge for a radio is given by P =40-4x^2 where x is the number (in millions) produced.
It costs the company $15 to make a radio.
:
a.) Write an expression for the company's total revenue in terms of x (Could you explain the process for finding this expression?)
:
Revenue = no. of radios sold * price of the radio
R(x) = x(40-4x^2)
R(x) = -4x^3 + 40x
:
:
b.) Write a function for the company's profit P by subtracting the total cost to make x radios from the expressions in Part A(the one just found)
:
Profit = Revenue - the total cost, (15x is the cost of all the radios sold)
P(x) = -4x^3 + 40x - 15x
P(x) = -4x^3 + 25x
:
:
c.) Currently, the company produces 1.5 million radios and makes a profit of $24,000,000.
Write and solve an equation to find a lesser number of radios that the company could sell and still make a profit.
:
Assume they make 1 million radios,
equation is in millions of radios and millions of dollars
P(x) = -4x^3 + 25x
x = 1 (million)
P(x) = -4(1^3) + 25(1)
P(1) = -4 + 25
P(x) = $21 million in profit when they make 1 million radios
;
d.) Do all the solutions in part c make sense in this situation? Explain.
:
Graphically we can explain it easily,
y = millions of dollars profit, x = millions of radios sold
Green line is $21 million
Looks like max profit occurs when 1.5 million are sold, do you agree?
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