Suppose the marginal cost function (=supply curve) for these cell phone subscriptions is given by:
p= C'(q)= 12.417 + 0.8884q
p= domain input q= output.
a) assume the fixed cost for these cell phone subscriptions is $435.60. Integrate the supply function above to find the cost function C(q).
I believe this to be: 0.4442q^2+12.41q-435.60
b) Now use both the cost function and the demand function to find the profit function for this situation. then find the number of subscriptions that will maximize profit as well as what the monthly subscription price and the maximum profit will be for this value of q.
Equations:
Marginal cost: p= C'(q)= 12.417 + 0.8884q
Believed cost function c(q)= 0.4442q^2+12.41q-435.60
Demand function= -.0166q^3 + -7.7405q^2 + -14.3634 + 148.3972
c) Now find a simplified formula for the average cost function (C(q)/q ). Then find the value of 'q' which will minimize this function. Find and state the monthly subscription price p that corresponds to this value of q; also find what the profit will be?
