A refrigerator manufacturer can sell all the refrigerators of a particular type that he can produce. The total cost of producing 'q' refrigerators per week is given by 300q+2000.the demand function is estimated as 500-2q.
[a] Derive the revenue function.
[b] Obtain the total profit function.
[c] How many units per week should be produced in order to maximize profit?
[d] What is the maximum profit available.

Question

A refrigerator manufacturer can sell all the refrigerators of a particular type that he can produce. The total cost of producing 'q' refrigerators per week is given by 300q+2000.the demand function is estimated as 500-2q.
[a] Derive the revenue function.
[b] Obtain the total profit function. 
[c] How many units per week should be produced in order to maximize profit?
[d] What is the maximum profit available.

dumbcow · Answer

revenue = price*quantity
p = 500-2q
revenue-> R(q) = 500q -2q^2

profit = revenue -cost
P(q) = R(q) -C(q) = (500q-2q^2)-(300q+2000)
P(q) = -2q^2 +200q -2000

anonymous · Answer

thanks very much dumbcow.

dumbcow · Answer

yw
about maximizing, find vertex of the parabola formed by P(q)

anonymous · Answer

ok.....

dumbcow · Answer

x = -b/2a  

max_q = -200/-4 = 50
plug that in to get max_profit

anonymous · Answer

am getting it

anonymous · Answer

pls dumbcow, how did u get the R[q]=500q-2q^2

dumbcow · Answer

oh sorry i multiplied p*q
(500-2q)*q

anonymous · Answer

ok...thanks