68. Break-Even The total revenue function for a home theater system is given by R 266x, and the total cost function for the system is C = 2000 + 46x + 2x², where R and C are each measured in dollars and x is the number of units produced and sold. boo a. Form the profit function for this product from the two given functions. b. What is the profit when 55 systems are produced and sold? c. How many systems must be sold to break even on this product? Igque

68. Break-Even The total revenue function for a home theater system is given by R 266x, and the total cost function for the system is C = 2000 + 46x + 2x², where R and C are each measured in dollars and x is the number of units produced and sold. boo a. Form the profit function for this product from the two given functions. b. What is the profit when 55 systems are produced and sold? c. How many systems must be sold to break even on this product? Igque

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter4: Systems Of Linear Equations

Section4.3: Solve Mixture Applications With Systems Of Equations

Problem 4.59TI: The manufacturer of a weight training bench spends $15 to build each bench and sells them for $32....

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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 weight training bench spends $15 to build each bench and sells them for $32. The manufacturer also has fixed costs each month of $25,500. (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.
2) A retailer determines that the cost of ordering and storing units of a product can be modelled by C(x)= 3x + 20000/x
3. A sporting goods store sells 64 tennis rackets per month at $90$ each. The owners estimate that for each $5 increase in price, they will sell 2 fewer tennis rackets per month. Find the price per tennis racket that will maximize revenue.
25. a car manufacturer estimated that the cost of production of x cars of a certain model is c=20x-0.05x2-600. How many should be reduced for minimum cost
An apple grower finds that if he plants 80 trees per acre, each tree will yield 26 bushels of fruit. He estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. Given a price of $1.00 per bushel, find the maximum revenue and how many trees should he plant per acre to maximize her harvest? 36 trees per acre, maximum revenue of $7,480 37 trees per acre, maximum revenue of $7,482 43 trees per acre, maximum revenue of $7,482 44 trees per acre, maximum revenue of $7,480
1.At what price should the company sell their product if they wish to make as much revenue as possible? How much revenue will they make?
6. A manufacturer estimates that the cost of production of “x” units of a certain item is C=40x-0.02x2-600. How many units should be produced for minimum cost?
(c) If Outland could lease the manufacturing facilities to another company for $25,000 per year, what would be the net total cost to outsource production of the part? Net cost to buy $ enter the net cost to buy in dollars (d) Should Outland outsource production of the part given the opportunity to lease the facilities? The Outland Company manufactures 5,000 units of a part that could be purchased from an outside supplier for $16 each. Outland’s costs to manufacture each part are as follows: Direct materials $4 Direct labor 3 Variable manufacturing overhead 6 Fixed manufacturing overhead 10 Total $23 All fixed overhead is unavoidable and is allocated based on direct labor. The facilities that are used to manufacture the part have no alternative uses.
1.) A retiree has 60 garden plots on which he could plant cabbage and pechay. His friend told him that he could make a profit of Php 100 per slot of cabbage and Php 90 per slot of pechay. His household could not possibly take care of more than20 plots of cabbage and 40 plots of pechay. How many plots of each vegetable should he plant for him to have a maximum profit? What is the maximum profit? 2.) A chemist makes a component of orchid fertilizer that requires two secret ingredients labeled as A and B. She sells ingredient A at Php 200 per kilogram and ingredient B at Php 350 per kilogram. Per production, a kilogram of ingredient A requires 4 units of special pollen while 3 units for each kilogram of ingredient B. Suppose the excess of ingredient B over ingredient A per production should be at most 4 units, and there are only 24 units of special pollen available per production, how many kilograms of ingredient A and ingredient B should be made per production to maximize the sales?
A company that makes thing-a-ma-bobs has a start-up cost of $ 7558. It costs the company $ 3.98 to make each thing-a-ma-bob. The company charges $ 4.69 for each thing-a-ma-bob. Let ? denote the number of thing-a-ma-bobs produced. Write the cost function for this company. ?(?)C(x) = Write the revenue function for this company. ?(?)R(x) = What is the minimum number of thing-a-ma-bobs that the company must produce and sell to make a profit? (Note: For this part, you will want to find the break-even point and then round to the next whole number.)
At a price of $28.75, producers will provide 9 items, while at a price of $34.25, they will provide 31 items. Consumers will purchase 86 of these items if the price is $91.5, but will purchase 132 items if the price decreases to $81.25. Find the market equilibrium point. (Enter your answers as a comma-separated list.)