Explanation Given: The marginal cost of extracting x tons of copper ore from a mine is 0.6 + 0.008 x in thousands of dollars per ton. The extracting amount of copper varies from a = 0 and b = 50 units for the first 50 tons. The extracting amount of copper varies from a = 50 units and b = 100 units for the next 50 tons. Start-up cost is $ 100 , 000 . Theorem used: Net change theorem: The integral of a rate of change is the net change is given by, ∫ a b F ′ ( x ) d x = F ( b ) − F ( a ) (1) Here, the lower limit is a and the upper limit is b . Calculation: Apply Net change Theorem as follows: The marginal cost for extraction of copper for the first 50 tons is obtained by the use of Net change Theorem as follows. Modify Equation (1) for the calculation of cost. ∫ a b C ′ ( x ) d x = C ( b ) − C ( a ) (2) Substitute 0 for a , 50 tons for b , and [ ( 0.6 + 0.008 x ) × 1 , 000 ] for C ′ ( x ) in equation (2). ∫ 0 50 ( 0.6 + 0.008 x ) 1 , 000 d x = C ( 50 ) − C ( 0 ) C ( 50 ) = 1 , 000 ∫ 0 50 ( 0.6 + 0.008 x ) d x + C ( 0 ) (3) Substitute $ 100 , 000 for C ( 0 ) in equation (3). C ( 50 ) = 1 , 000 ( 0.6 x + 0.008 x 2 2 ) 0 50 + $ 100 , 000 = 1 , 000 × [ ( 0

9th Edition

ISBN: 9781337613927

Author: Stewart

Publisher: CENGAGE L

See similar textbooks

Question

Chapter 8.4, Problem 3E

To determine

To calculate: The cost of extracting the first 50 tons of copper and to find the cost of extracting the copper from 50 tons to 100 tons.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.4, Problem 2E

Chapter 8.4, Problem 4E

Students have asked these similar questions

A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by P'(t) = (5t + 15) (t² + 6t+9) ³. (a) Find the total profit in the first three years. (b) Find the profit in the sixth year of operation. (c) What is happening to the annual profit over the long run? (a) The total profit in the first three years is $ (Round to the nearest dollar as needed.)

Find the area between the curves. x= -2, x = 7, y=2x² +3, y=0 Set up the integral (or integrals) needed to compute this area. Use the smallest possible number of integrals. Select the correct choice below and fill in the answer boxes to complete your choice. A. 7 [[2x² +3] dx -2 B. [[ ] dx+ -2 7 S [ ] dx The area between the curves is (Simplify your answer.)

The rate at which a substance grows is given by R'(x) = 105e0.3x, where x is the time (in days). What is the total accumulated growth during the first 2.5 days? Set up the definite integral that determines the accumulated growth during the first 2.5 days. 2.5 Growth = (105e0.3x) dx 0 (Type exact answers in terms of e.) Evaluate the definite integral. Growth= (Do not round until the final answer. Then round to one decimal place as needed.)

Chapter 8 Solutions

Calculus, Early Transcendentals

Ch. 8.1 - Use the arc length formula (3) to find the length...Ch. 8.1 - Use the arc length formula to find the length of...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Find the exact length of the curve. 9....Ch. 8.1 - Find the exact length of the curve. 10....

Knowledge Booster

The cost of extracting the first 50 tons of copper and to find the cost of extracting the copper from 50 tons to 100 tons.

Solution Summary: The author calculates the cost of extracting the first 50 tons of copper from a mine by using the Net change theorem.

To calculate: The cost of extracting the first 50 tons of copper and to find the cost of extracting the copper from 50 tons to 100 tons.

Want to see the full answer?

Chapter 8 Solutions