Question

44. A firm determines that x units of its product can be sold daily at p dollars per unit, where x = 1000 - p The cost of producing x units per day is C(x) = 3000 + 20x (a) Find the revenue function R(x). (b) Find the profit function P(x). (c) Assuming that the production capacity is at most 500 units per day, determine how many units the company must produce and sell each day to maximize the profit. (d) Find the maximum profit. (e) What price per unit must be charged to obtain the maximum profit?

Uploaded: 2022-04-08T06:24:45-08:00
Duration: 7 min 18 s
Channel: Maitreya E

          44. A firm determines that x units of its product can be sold daily at p dollars per unit, where x = 1000 - p The cost of producing x units per day is C(x) = 3000 + 20x (a) Find the revenue function R(x). (b) Find the profit function P(x). (c) Assuming that the production capacity is at most 500 units per day, determine how many units the company must produce and sell each day to maximize the profit. (d) Find the maximum profit. (e) What price per unit must be charged to obtain the maximum profit?

44. A firm determines that x units of its product can be sold daily at p dollars per unit, where x = 1000 - p The cost of producing x units per day is C(x) = 3000 + 20x (a) Find the revenue function R(x). (b) Find the profit function P(x). (c) Assuming that the production capacity is at most 500 units per day, determine how many units the company must produce and sell each day to maximize the profit. (d) Find the maximum profit. (e) What price per unit must be charged to obtain the maximum profit?

Added by Juan Francisco M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Maitreya E

04/08/2022

Step 1

Substituting p into the equation, we get R(x) = x * (1000 - x) = 1000x - x^2. Show more…

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A firm determines that x units of its product can be sold daily at p dollars per unit, where x = 1000 - p. The cost of producing x units per day is C(x) = 3000 + 20x. (a) Find the revenue function R(x). (b) Find the profit function P(x). (c) Assuming that the production capacity is at most 500 units per day, determine how many units the company must produce and sell each day to maximize the profit. (d) Find the maximum profit. (e) What price per unit must be charged to obtain the maximum profit?