high school senior year project

Question

We're putting together a project that combines two subjects: math and business, and we'd like to have a math problem. The use of derivative functions is needed. Would you be able to assist us with a math problem and its solution? Our subject matter is dependent on (profit, cost and revenue)

Answer 1

R(x) = 100x

C(x) = 30x +10x^2 + 200

C'(x) = 20x+30 = R'(x) = 100

20x = 70

x = 70/20 = 3.5

output level of 3.5 maximizes profit or minimizes loss

P(x) = R(x)-C(x) = 350 - 30(3.5)- 10(12.25) -200

=150-122.5-105

=45-122.5

=- 77.5

Minimum Loss = $77.50

business decision is to go bankrupt, shut down or stay in business?

in the short run a $77.50 loss is less than the $200 fixed cost of shutting down

in the long run, sell the business, be more efficient, cut costs or do bankruptcy