Question

Given cost and price​ (demand) functions C(q)=100q+41,000 and p(q)=−2.1q+850​, what is the maximum revenue that can be​ earned?

It would be:

A company produces a special new type of TV. The company has fixed costs of $460,000​, and it costs $1000 to produce each TV. The company projects that if it charges a price of $2600 for the​ TV, it will be able to sell 850 TVs. If the company wants to sell 900 ​TVs, however, it must lower the price to $2300. Assume a linear demand. What price should be set to earn maximum profits?

Answer 1

We have the following information

Demand: p = 850 – 2.1q; where q is output and p is the price

Total revenue = Price × Output

Total revenue = (850 – 2.1q)q

Total revenue (TR) = 850q – 2.1q²

Taking the first derivative of the TR

ΔTR/Δq = 850 – 4.2q = 0

850 – 4.2q = 0

850 = 4.2q

q = 202.38

Taking the second derivative

Δ²TR/Δq² = – 4.2 < 0

So, the TR is maximized for q = 202.38

TR for q = 202.38

TR = (850 × 202.38) – 2.1(202.38)²

TR = 172023 – 86011

So, the maximum revenue that can be earned is 86,012