The cost function for a certain company is C=60x+300 and the revenue

Question

The cost function for a certain company is

C = 60 x + 300

and the revenue is given by

R = 100 x - 0.5 x^{2}

Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of

$ 300

.

Answer 1

Step 1

P (x) = R (x) - C (x)

Where P = Profit Function, C = cost function, R = revenue function
Step 2

R (x) - C (x) = 300

\Rightarrow 100 x - 0.5 x^{2} - 60 x - 300 = 300

\Rightarrow 40 x - 0.5 x^{2} - 600 = 0

\Rightarrow 40 x - \frac{5}{10} x^{2} - 600 = 0

\Rightarrow 400 x - 5 x^{2} - 6000 = 0

\Rightarrow 5 x^{2} - 400 x + 6000 = 0

\Rightarrow x^{2} - 80 x + 1200 = 0

\Rightarrow x^{2} - 60 x - 20 x + 1200 = 0

\Rightarrow x (x - 60) - 20 (x - 60) = 0

\Rightarrow (x - 60) (x - 20) = 0

Rither,

x - 60 = 0

\Rightarrow x = 60

or,

x - 20 = 0

x = 20

∴

The two values of x with be 60, 20 that with create a profit of Rs 300

Expert Answer