Current Attempt in ProgressA fertilizer producer finds that it can sell its product at a price of p = 3500 - 0.7r dollars per unit when it produces x units offertilizer. The total production cost (in dollars) for x units isC(x) =105,000 + 875x + 0.175x-.If the production capacity of the firm is at most 1000 units of fertilizer in a specified time, how many units must be manufactured andsold in that time to maximize the profit?Selling iunits maximizes profit.

Profit, pro(x) = xP - C(x)For maximum profit, put dpro(x)dx = 0

Answered: A fertilizer producer finds that it can…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter8: Functions

Section8.CR: Review Problem Set

Problem 50CR

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Similar questions

The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8,000. (a) Find the cost function C when x energy drinks aremanufactured. (b) Find the revenue function R when x drinks are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the breakeven point means.
The manufacturer of a water bottle spends $5 to build each bottle and sells them for $10. The manufacturer also has fixed costs each month of $6500. (a) Find the cost function C when x bottles are manufactured. (b) Find the revenue function R when x bottles are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the break-even point means.
The manufacturer of a weight training bench spends $120 to build each bench and sells them for $170. The manufacturer also has fixed costs each month of $150,000. (a) Find the cost function C when x benches are manufactured. (b) Find the revenue function R when x benches are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the break-even point means.
Sales A soft-drink vendor at a popular beach analyzes his sales records and find that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x)=0.001x2+3x1800 What is his maximum profit per day, and how many cans must he sell for maximum profit?
Agriculture At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 700 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So, the number of pounds of grapes produced per acre is modeled by An=700+n10-0.01n where n is the number of additional vines planted. Find the number of vines that should be planted to maximize grape production.

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