A company has a monopoly on the manufacture and selling of theorets. The cost of making x theorets is ?0.1x^2 + 100x + 8000 dollars. Suppose that the company sets a price of ?0.05x + 150 dollars per theoret, when there is a demand for x theorets per month. In January of 2011, the company made and sold 400 theorets.
(1) Write expressions for the cost C(x) and the marginal cost, C?(x), of manufacturing x theorets.
For this question, I am assuming that C(x) = -0.1x^2 + 100x + 8000, and that marginal cost is the derivative of C(x), which would be C'(x) = -0.2x + 100
I am not sure about these answers though, so if someone could verify them, i would appreciate it
(2) Compute the marginal average cost
For this, first i found the average cost, which is (-0.1x^2 +100x+8000) / x >>>simplified to -0.1x + 100 + (8000/x)
Then, to find marginal average cost, all i did was find the derivative of the average cost function, which turns out to be : -0.1 - (8000 / x)
The next few questions is where i have trouble:
(3) The company is considering increasing the number of theorets made and sold for February 2010. Use your above answer to estimate the change in the average cost of manufacture, for each additional theoret made in February.
(4) Compute the profit P(x) and the marginal profit when x theorets per month are being made and sold.
(5) About how much more profit will the company make in February 2011 than in January 2011, if it makes and sells 403 theorets in February? (Use part your answer to part (4) to do this.)
Thanks for any help!
(1) Write expressions for the cost C(x) and the marginal cost, C?(x), of manufacturing x theorets.
For this question, I am assuming that C(x) = -0.1x^2 + 100x + 8000, and that marginal cost is the derivative of C(x), which would be C'(x) = -0.2x + 100
I am not sure about these answers though, so if someone could verify them, i would appreciate it
(2) Compute the marginal average cost
For this, first i found the average cost, which is (-0.1x^2 +100x+8000) / x >>>simplified to -0.1x + 100 + (8000/x)
Then, to find marginal average cost, all i did was find the derivative of the average cost function, which turns out to be : -0.1 - (8000 / x)
The next few questions is where i have trouble:
(3) The company is considering increasing the number of theorets made and sold for February 2010. Use your above answer to estimate the change in the average cost of manufacture, for each additional theoret made in February.
(4) Compute the profit P(x) and the marginal profit when x theorets per month are being made and sold.
(5) About how much more profit will the company make in February 2011 than in January 2011, if it makes and sells 403 theorets in February? (Use part your answer to part (4) to do this.)
Thanks for any help!
