Manufacturing—Bicycles: For Exercise, the Wheelex Company manufactures bicycles and finds...

Manufacturing—Bicycles: For Exercise, the Wheelex Company manufactures bicycles and finds the price function for the bicycles to be

 p(x) = −0.02x + 190

where x represents the number of bicycles produced and sold and p(x) is the price of the bicycle. Furthermore, the fixed and variable costs to produce x bicycles are $5600 and $85 per bicycle, respectively.

Use the solution from part (a) of Exercise 1 with the solution to part (a) of Exercise 2 to complete parts (a) and (b).

(a) Derive the profit function P(x).

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(b) If the bicycles must be manufactured in lots of 250, how many bicycles should be manufactured so that the profit is as large as possible? Verify your answer by completing the table.

Manufacturing—Bicycles: For Exercises 1–2, the Wheelex Company manufactures bicycles and finds the price function for the bicycles to be

 p(x) = −0.02x + 190

where x represents the number of bicycles produced and sold and p(x) is the price of the bicycle. Furthermore, the fixed and variable costs to produce x bicycles are $5600 and $85 per bicycle, respectively.

Exercise 1–2

1. The cost function follows the linear form C(x) = mx + b. Answer the following.

(a) Write the cost C in the linear form C(x) = mx + b.

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(b) Use calculus to compute the marginal cost function .

2. Use p(x) and the cost function information given in Exercise 1 to complete parts (a) through (c).

(a) Derive the revenue function R(x).

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(b) Use calculus to compute .

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(c) Evaluate MR (500) and interpret.