Demand Function, Q=280000−400p
Inverse Demand Function, P=400280,000−Q=700−400Q
Total Revenue=Price⋅Quantity=700−400Q⋅Q=700Q−400Q2
Marginal revenue function=dQd(700Q−400Q2)=700−0.005Q
Total Cost function=350000+300Q+0.0015Q2
Marginal Cost=dQd(350000+300Q+0.0015Q2)=300+0.003Q
Profit is maximized when Marginal Cost = Marginal Revenue (Price):
300+0.003Q=700−0.005Q
0.003Q+0.005Q=700−300
0.008Q=400
Q=0.008400=50000
i) The firm should produce 50000 units to maximize its profit
ii) Price that should be charged = Marginal Revenue at 50000 units of output = $(700−0.005(50000))=$(700−250)=$450
iii)At maximum profit condition, Q=50000
Total Revenue=700Q−0.005Q2=700x50000−0.005⋅500002=$22500000
Total Cost=350000+300Q+0.0015Q2= =350000+300⋅50000+0.0015⋅500002=$19100000
Annual Profit=Total Revenue−Total Cost=$22500000−$19100000=$3400000
Therefore, expected annual profit = $3400000
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