The total cost a product is defined by the expression TC=0.001q3-0.025q2+5q+100.
ID: 1213167 • Letter: T
Question
The total cost a product is defined by the expression TC=0.001q3-0.025q2+5q+100. If the price of the product is $115.00. determine the optimal quantity to produce and sell. At that level of operation, compute marginal cost, total cost, total variable cost, average total cost, average variable cost. Revenue and profits Compute the first two years of the study of a present value for the following project. The initial investment is one million dollar. The life of the project is 7 years, depreciated with MACRS class 5 years. The salvage is 255.000. MARR is 15% and tax rate 35%. The project will have financial support of the bank of 40% of initial investment, payable yearly, with 10% interest rate for 5 years. saving per year are estimated at 450000 the first 5 years and 275000 the last two years.Explanation / Answer
Answer:
The total cost (TC) is: TC = 0.001q3 -0.025q2 +5q + 100
Price of the product is: $115
We know formulae:
TC = TFC + TVC
MC = TC/Q
AFC = TFC/Q
AVC = TVC/Q
ATC = AFC + AVC
Marginal Cost (MC) = dTC/dq
MC = 0.003 q2 – 0.05q + 5
We know, MC = P
115 = 0.003 q2 – 0.05q + 5
= 0.003 q2 – 0.05q - 110
We can solve the quadratic equation, then we get q = 200
Now we can substitute q = 200 into the TC and MC function.
Total Cost (TC) = 0.001(200)3 -0.025(200)2 +5(200) + 100
= 8000 – 1000 + 1000 + 100
= $8,100
Marginal Cost (MC) = 0.003(200)2 – 0.05(200) + 5
= 120 – 10 + 5
= $115
Total Variable Cost (TVC) = 0.001(200)3 -0.025(200)2 +5(200)
= 8000 – 1000 + 1000
= $8,000
Average Total Cost (ATC) = 8100/200
= $40.5
Average Variable Cost (AVC) = 8000/200
= $40
Revenue = P x Q = 115 x 200 = $23,000
Profits = TR – TC = $23,000 - $8,100 = $14,900
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