A company has revenue given by Rx 564 X dollars and a total

A company has revenue given by R(x) = 564 X dollars and a total cost given by C(X) = 40,000 + 64X dollars, where X is the number of units produced and sold. The profit can be found by forming the function P(X) = R (X) - C(X). Write the Profit Function. Find the Profit when 120 units are produced and sold. How many units give break-even?

Solution

a)

Profit function P(X) = R(X) - C(X)

P(X) = 564X - 40000-64X

P(X) = 500X - 40000 is the profit function

b)

when 120 units are produced

The profit at X = 120

P(120) =   500* 120 - 40000 = 20000

C)   

The \"break-even point\" is when: \"cost\" = \"revenue\"

40000 + 64X = 564X

=> 500X = 40000

=> X = 80

80 units give break-even