Qustion A:Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.)P(x) = −0.003x2 + 6x − 5,000Increasing: _____________ Decreasing: _____________ Qustion B:Minimizing Average Cost The total monthly cost (in dollars) incurred by a certain guitar manufacturer in manufacturing x units of its Professional Series guitars is given by the functionC(x) = 0.002x2 + 150x + 32000.(a)Find the average cost function C.C = ______________(b)Determine the production level that will result in the smallest average production cost.x = _____________ Qustion C:Maximizing Profits The weekly demand for DVDs manufactured by a certain media corporation is given byp = −0.0003x2 + 55where p denotes the unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with producing these discs is given byC(x) = −0.001x2 + 13x + 4500where C(x) denotes the total cost (in dollars) incurred in pressing x discs. Find the production level that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula. (Round your answer to the nearest integer.)x = _______________ DVDs

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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.2: Graphs

Problem 15E

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Qustion A:

Profit Function for Producing Thermometers

The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.)

P(x) = −0.003x² + 6x − 5,000

Increasing: _____________

Decreasing: _____________

Qustion B:

Minimizing Average Cost

The total monthly cost (in dollars) incurred by a certain guitar manufacturer in manufacturing x units of its Professional Series guitars is given by the function

C(x) = 0.002x² + 150x + 32000.

(a)

Find the average cost function C.

C = ______________

(b)

Determine the production level that will result in the smallest average production cost.

x = _____________

Qustion C:

Maximizing Profits

The weekly demand for DVDs manufactured by a certain media corporation is given by

p = −0.0003x² + 55

where p denotes the unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with producing these discs is given by

C(x) = −0.001x² + 13x + 4500

where C(x) denotes the total cost (in dollars) incurred in pressing x discs. Find the production level that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula. (Round your answer to the nearest integer.)

x = _______________ DVDs

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