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If C = 0.0001Q2 + 3Q + 6000 is a total-cost function, find the marginal cost when Q = 100.
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- The function C(x)=−24x+1936 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $20?The estimated cost to produce x items is given by the function: C(x) = 0.004x² + 5x + 6000 Determine the average cost and marginal cost of producing 2,000 items and calculate the level of output for which the average cost is the lowest and what that cost is.The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 150 + 2,600x – 0.06x2. (a) Find the marginal cost function C'(x). C'(x) = (b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars. The cost to air the 5th commercial is approximately X dollars. (c) What is the exact cost to air the 5th commercial? Convert your answer to dollars. The exact cost to air the 5th commercial is x dollars.
- Use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.) C = 8950x + 220,000, R = 9857xthe cost of producing 5-gallon water bottles is given by C(q)=0.005^2+2q+1000. If 2000 5-gallon water bottles are produced find the, (i) total cost (ii) average cost (iii)marginal cost (iv) marginal average costIf the number of miles for a delivery is 5 & the number of minutes is 30, what is the estimated overhead cost associated with that delivery rounded to two decimals?
- The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 3,000x + 0.09x² (a) Find the marginal cost function C'(x). HINT (See Example 1.] C'(x) = Use it to estimate how fast the cost is Increasing when x- 4. thousand dollars per television commercial Compare this with the exact cost of alring the fifth commercial. The cost is going up at the rate of $ per television commercial. The exact cost of airing the fifth commercial is $ Thus, there is a difference of $ (b) Find the average cost function C, and evaluate C(4). HINT [See Example 2.] C(x) = C(4) - thousand dollars per television commercial What does the answer tell you? The average cost of airing the first four commercials is $ per commercial.K Drilling of an oil well has a fixed cost of $40,000 and a marginal cost of M'(x) = 5000+56x dollars per foot, where x is the depth in feet. Find the expression for M(x), the total cost of drilling x feet. [Note M(0) = 40,000] M(x)=Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is C(x)=7000+6x+0.01x^2+0.0002x^3. (a) Find the marginal cost function. (b) Find the marginal cost at x=100 (c) Find the cost at x=100
- Consider the following function: Ĉ = 0.03q + 6 + 200/q - determine the approximate cost to increase production from 200 units to 201 units - determine the function of marginal costAssume that it costs a company approximately C(x) = 400,000 + 160x + 0.003x² dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) (10,000) = = per smartphone. The exact cost of producing the 10,001st smartphone is $ $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- than the average cost from (b). This means that the average cost is ---Select--- Thus, there is a difference of $ at a production level of 10,000 smartphones.The cost of producing 5-gallon water bottles is given by: C(q) = 0.005q + 2q + 1000. If 2000 5-gallon water bottles are produced,find the total cost, average cost, marginal cost,marginal average cost.
