Profit Maximization Given: Inverse Demand Function P = 1000 - 5Q Therefore margi

Question

Profit Maximization Given: Inverse Demand Function P = 1000 - 5Q Therefore marginal revenue equals to: MR = 1000 - 10Q Cost of producing at facility 1: C1(Q1) = 10,050 + 5Q21 Therefore marginal cost at facility 1 equals to: MC1 = 10Q1 Cost of producing at facility 2: C2(Q2) = 5,000 + 2Q22 Therefore marginal cost at facility 2 equals to: MC2 = 4Q2 Profit maximization occurs where MR = MC therefore: MR = 1000 - 1O(Q1 + Q2) = 1OQ1 MR = 1000 - 10(Q1 + Q2) = 4Q2 Next we solve for Q1 and Q2 respectively:

Explanation / Answer

1000-10(Q1+Q2)=10Q1--------eqn1 1000-10(Q1+Q2) =4Q2----------eqn2 taking all Q1 and Q2 on one side in eqn 1 and 2 we get 1000=10Q1 + 10Q1 +10Q2--------1 1000= 4Q2 +10Q1 +10Q1----------2 1000=20Q1 + 10Q2 ------1 1000=10Q1+14Q2 ------2 multiplying eqn2 with and substracting eqn2 we get 2000-1000 = 20Q1-20Q1+28Q2-10Q2 1000=18Q2 Q2=1000/18 = 55.55 putting value of Q2 in eqn 2 we get 1000=10Q1+14*55.55 10Q1= 1000-777.77 Q1=22.22

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