8. The price p (in dollars) and the demand x for a particular wool sweater are...

8. The price p (in dollars) and the demand x for a particular wool sweater are related by the equation p = 100 − 0.025x a. Find the domain of this function. Show all work and clearly label the answer below. b. Find the revenue R (x) = x · p , from the sale of x wool sweaters and state the domain of the function R (x) . c. Find the marginal revenue at a production level of 1,600 sweaters and interpret the results. Show all work and clearly label the answer below. d. Find the marginal revenue at a production level of 2,500 sweaters and interpret the results. Show all work and clearly label the answer below.

Expert Solution

The domain of a function is the set of numbers that can go into a given function. In other words, it is the set of x-values that you can put into any given equation.

milcah answered 2 years ago

A price p (in dollars) and demand x for a product are related by 2 x^2...

A price p (in dollars) and demand x for a product are related by 2 x^2 + 2 x p + 50 p^2 = 20600. If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand. Rate of change of demand

The Sweater Company produces sweaters. The company buys raw wool on the market and processes it...

The Sweater Company produces sweaters. The company buys raw wool on the market and processes it into wool yarn from which the sweaters are woven. One spindle of wool yarn is required to produce one sweater. The costs and revenues associated with the sweaters are given below: Per Sweater Selling price P30.00 Cost to manufacture: Raw materials: Buttons, threads, lining P 2.00 Wool yarn 16.00 Total raw materials 18.00 Direct labor 5.80 Manufacturing overhead 8.70 32,50...

The price-demand equation for a particular product is f(p)=850−3p2. At a price of $14 is this...

The price-demand equation for a particular product is f(p)=850−3p2. At a price of $14 is this product elastic, inelastic, or unit elastic?

The price-demand equation for a particular product is f(p)=850−3p2. The elasticity of demand of this product...

The price-demand equation for a particular product is f(p)=850−3p2. The elasticity of demand of this product at a price of $13 is?

8. [Own Price Elasticity of Demand] Given a demand function Q = f(P), the own price...

8. [Own Price Elasticity of Demand] Given a demand function Q = f(P), the own price elasticity of demand is defined as ? = (dQ/dP) · (P/Q) What is the own price elasticity of demand ? (a) for the linear demand function Q = 100?5P when P = 10. (b) for the linear inverse demand function P = 100?4Q when (i) Q = 10; (ii) Q = 20; (iii) Q = 12.5. (c) for the demand function Q = P...

Demand for good X is X = 100 – 4P, where P is the market price...

Demand for good X is X = 100 – 4P, where P is the market price of X. A monopolist supplies this market and has a cost function 5X. When the monopolist produces his optimal level of X, what is the resulting deadweight loss in the economy? Could you draw the graph with curves? (a.) $180 (b.) $200 (c.) $222 (d.) $285

The Scottie Sweater Company produces sweaters under the “Scottie” label. The company buys raw wool and...

The Scottie Sweater Company produces sweaters under the “Scottie” label. The company buys raw wool and processes it into wool yarn from which the sweaters are woven. One spindle of wool yarn is required to produce one sweater. The costs and revenues associated with the sweaters are given below: Per Sweater Selling price $ 36.00 Cost to manufacture: Raw materials: Buttons, thread, lining $ 2.00 Wool yarn 18.00 Total raw materials 20.00 Direct labor 8.20 Manufacturing overhead 12.30 40.50 Manufacturing...

The demand for mysterious good X in Lansing is Q=12-P, where P is the price of...

The demand for mysterious good X in Lansing is Q=12-P, where P is the price of good X per pound and Q is the quantity demanded in pounds. The marginal cost of producing the good is $2 per pound. There is no fixed cost of producing the good. There are two firms, Alice and Bob, who can produce the good. A) Find Alice's best response function. B) Find Bob's best response function. C) Find each firm's Nash equilibrium quantity. D)...

The demand function for a particular product is given by D(x)=3x2−7x+110‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√D(x)=3x2−7x+110 dollars, where x is the...

The demand function for a particular product is given by D(x)=3x2−7x+110‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√D(x)=3x2−7x+110 dollars, where x is the number of units sold. What is the marginal revenue when 44 items are sold? Round your answer to 2 decimal places. D(x)=3x2−7x+110‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√t thats a suqare root over the numbers

Data for age (in years) and price (in hundreds of dollars) for a particular brand of...

Data for age (in years) and price (in hundreds of dollars) for a particular brand of car are provided in the accompanying data table. Presume that the assumptions for regression inferences have been met. Complete parts (a) through (d) below using the given data. X (age) 6, 6, 6, 2, 2, 5, 4, 5, 1, 4 Y (price) 289, 280, 293, 428, 382, 315, 355, 326, 423, 322 A) Obtain a point estimate for the mean price of all 3-year...

Question