Question

In: Math

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.

Solutions

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.


Related Solutions

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...
Given the demand function for a particular product is q(p)=(10-p^2)e^-p+3 for price p in thousands of...
Given the demand function for a particular product is q(p)=(10-p^2)e^-p+3 for price p in thousands of dollars. Suppose the cost of producing q units of this particular product is In(q). a) Find the profit function in terms of p, pie(p). Use log properties to simplify the function. b) Show there exists a solution p where pie(p)=0. (Cite any theorems used and do not solve for p) c) Suppose we are current charging $3000 and we want to increase profit by...
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 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 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...
1.) The demand model p=0.02x+19 gives the price per model (in dollars per novel) p when...
1.) The demand model p=0.02x+19 gives the price per model (in dollars per novel) p when novels are sold. The cost (in dollars) for publishing x novels is given by C(x)=4x+19. a.)How many novels should be sold in order for revenue to be a maximum? b.)What is the maximum profit? c.) Find the average cost when 50 novels are sold.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT