Demand The demand function for a product is given by3p = 8,000 1-8,000(1-3 + e-0.004xwhere p is the price per unit (in dollars) and x is the number of units sold. (Round your answers to the nearest whole number.)(a) Find the number of units sold when p = $400.units(b) Find the number of units sold when p = $1,300.units Minimum Average Cost The cost of producing x units of a product is modeled byC = 220 + 75x-320 In(x), x≥ 1.(a) Find the average cost function C.C(x) ==x2(b) Find the minimum average cost analytically. Use a graphing utility to confirm your result. (Round your answer to two decimal places.)

Demand The demand function is given as a) Substitute p = 400 into the demand function By taking…

Answered: Demand The demand function for a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 43E

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The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. b.What is the cost of making 25 items? c.Suppose the maximum cost allowed is SI500. What are the domain and range of the cost function, C(x) ?
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Cost Analysis A rival company manufactures fuel tanks for cars using a different production technique. The total weekly cost (in dollars) of producing x tanks is given by.. C(x) = 10000 +90x-0.05x2 %3D Find the marginal cost at a production level of 500 fuel tanks per week to approximate the cost of the 501st unit (Round to the nearest 2 decimal places, if needed) HINT: Steps to find the approximate or estimate (cost/revenue/profit) 1. Find C' (x) = MC (500); 2. take the derivative of the cost/revenue/profit function; 3. plug in 500 for x ASUS
Marginal Average Cost for Producing Thermometers The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing x thermometers is represented by the following function. Find the following functions (in dollars) and interpret your results. C(x) = 2,000 + 2x (a) Find the average cost function C. C(x) = (b) Find the marginal average cost function C'. C'(x) = (c) Interpret your results. O Since the marginal average cost function is negative for x > 0, the rate of change of the average cost function is negative for all x > 0. O Since the marginal average cost function is negative for x > 0, the rate of change of the average cost function is positive for all x > 0. O Since the marginal average cost function is positive for x > 0, the rate of change of the average cost function is positive for all x > 0. O Since the marginal average cost function is positive for x > 0, the rate of…
Marginal Average Cost Analysis A small machine shop manufactures drill bits used in the petroleum industry. The manager re-estimates that the total daily cost (in dollars) of producing X bits is ... C(X) = 1,000 + 25X – 0.05X² %3D Find the marginal average cost of producing 10 units. (Round to the nearest 2 decimal places, if needed) ASUS f3 f4 f5 f7 f8 f9 f10 f11 f6 X V. & 3. 4 7 8. 9. 16 图图

Unit name: Characteristics of function
Super Bowl Ads A minute ad during Super BowlVII in 1973 cost $200,000. The price tag for a30-second ad slot during the 2011 Super Bowlwas $3 million. The cost of a 30-second slot ofadvertising for the Super Bowl can be modeled byy = 0.0000966(1.101x ), where x is the number ofyears after 1900 and y is the cost in millions.a. According to the model, what was the cost of a30-second Super Bowl ad in 2000?b. The cost of a 30-second ad during Super Bowl XLIXin 2015 was $4.5 million. Does the model underestimate or overestimate the cost of these ads?
Cost The marginal cost for a catering service to cater to x people can be modeled by 20x dC dx x2 + 1,616 When x = 200, the cost C (in dollars) is $4,080.00. (a) Find the cost function. (b) Find the costs (in dollars) of catering to 500 people and 1,000 people. (Round your answers to two decimal places.) 500 people 1,000 people
The rate of growth G in the weight of a fish is a function of the weight w of the fish. For the North Sea cod, the relationship is given by G = 2.1w2/3 − 0.6w. Here w is measured in pounds and G in pounds per year. The maximum size for a North Sea cod is about 40 pounds. (a) Make a graph of G against w. (b) Find the greatest rate of growth among all cod weighing at least 9 pounds. (Round your answer to two decimal places.) pounds per year(c) Find the greatest rate of growth among all cod weighing at least 28 pounds. (Round your answer to two decimal places.) pounds per year
Directions: Show all work in a neat and organized manner. Be sure to use correct notation and use equal signs appropriately. Clearly indicate your answers. 1. Let the total cost function C(x) be C(x) = 0.0002x³ -0.07x2 +90x+ 5,600 (a) Find the average cost function C. (b) Find the marginal average cost function '.
Describe what fixed costs and marginal costs mean to a company. Choose the correct answer below. A. Fixed cost is the rate of change of cost C(x) at the level of production x and is equal to the slope of the cost function at x. Marginal cost is the constant for a particular product and does not change as more items are made. O B. The number of units at which revenue just equals cost is the fixed cost. Marginal cost is the constant for a particular product and does not change as more items are made. O C. Fixed cost is the constant for a particular product and does not change as more items are made. Marginal cost is the rate of change of cost C(x) at the level of production x and is equal to the slope of the cost function at x. OD. Fixed cost is the constant for a particular product and does not change as more items are made. The number of units at which revenue just equals cost is the marginal cost.
Demand The demand function for a product is given by p = 8,000(1-30-0.004x) where p is the price per unit (in dollars) and x is the number of units sold. (Round your answers to the nearest whole number.) (a) Find the number of units sold when p = $500. units (b) Find the number of units sold when p = $1,100. units

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