I did not know where you gor the 50 from in the similar equation

Question

For a certain company, the cost function for producing x items is C(x)=30x+100 and the revenue function for selling x items is R(x)=-0.5(x-100)^2+5,000. The maximum capacity of the company is 140 items. A.) Assuming that the company sells all that it produces, what is the profit function? Solve. P(x)= B.) What is the domain of P(x) C.) The company can choose to produce either 70 or 80 items. what is their profit for each. Profit when producing 70 items= Profit for producing 80 items= D.) can you explain from the model, why the company makes less profit when producing 10 more units.​

Answer 1

Profit = R-C = -.5(x-100)^2 + 5000 -30x -100

for x=70 R-C = -.5(30^2 -2100 +4900 = 2350

for x = 80 R-C = .-5(20^2 - 30(80) +4900 = 2300

max profit is when R'-C'=0 = -x+100-30 or x=70

the profit function is a parabola with maximum point at x=70

any output level less than or more than 70 will have lower profit

domain is zero to 140,