Elasticity of Demand The demand equation for a certain product is 4x + 2p - 20 - 0, where p is the unit price and x is the quantity demanded of the product. Find the elasticity of demand and determine whether the demand is elastic or inelastic, at the indicated prices. (a) p-9 E(9) - the demand is Select-. (b) p- 2 E(2) = the demand is Select- (c) p-5 E(5) = the demand is Select-

Elasticity of Demand The demand equation for a certain product is 4x + 2p - 20 - 0, where p is the unit price and x is the quantity demanded of the product. Find the elasticity of demand and determine whether the demand is elastic or inelastic, at the indicated prices. (a) p-9 E(9) - the demand is Select-. (b) p- 2 E(2) = the demand is Select- (c) p-5 E(5) = the demand is Select-

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.6: Optimization

Problem 11E: Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the...

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Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.
Application of derivative Optimization We are going to fence in a rectangular field that encloses 200 m2. If the cost of the material for of one pair of parallel sides is $3/m and cost of the material for the other pair of parallel sides is $8/m determine the dimensions of the field that will minimize the cost to build the fence around the field.
Equilibrium points for this nonlinear system follow a curve defined by an equation y=f(x) How do we find the function containing all the equilibrium points?
Application of derivative Optimization We are going to fence in a rectangular field. Starting at the bottom of the field and moving around the field in a counter clockwise manner the cost of material for each side is $6/ft, $9/ft, $12/ft and $14/ft respectively. If we have $1000 to buy fencing material determine the dimensions of the field that will maximize the enclosed.
Producers' Surplus The demand function for a certain brand of CD is given by p = −0.01x2 − 0.2x + 16 where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. The supply function is given by p = 0.01x2 + 0.8x + 4 where p is the unit price in dollars and x stands for the quantity that will be made available in the market by the supplier, measured in units of a thousand. Determine the producers' surplus if the market price is set at the equilibrium price. (Round your answer to the nearest dollar.)
The long run. A chair manufacturer hires its assembly-line labour for $18 an hour and calculates that the rental cost of its machinery is $6 per hour. Suppose that a chair can be produced using 4 hours of labour or machinery in any combination. The firm is currently using 1 hour of labour for every 3 hours of machine time. (Assume that labour is on the horizontal axis and capital is on the vertical axis). 3. Graphically illustrate your answer by drawing an isoquant, an isocost line for the current combination of labour and capital and an isocost line for the optimal combination of labour and capital. An isocost corresponding to the optimal combination of labour and capital is [a vertical line, a horizontal line, an upward sloping straight line, an upward sloping curve which is not a straight line, a downward sloping straight line, a downward sloping curve which is not a straight line, L-shaped] has slope [ ] at the optimal combination of inputs An isoquant…
The total production P of a certain product depends on the amountL of labor and the amount K of capital investment. If the cost of a unit of labor is m and the cost of a unit of capital is n , and the company can spend only p dollars as its total budget, then maximizing the production P is subject to mL=nK = p. Show that the maximum production occurs when L= (αp)/m , K= ((1-α)p)/n Note that P= bLαK1-α , 0<α<1
A demand function for a product is P = 100 – 2.2Q and its supply function is P = 2.8Q, where P is theprice of the product in pound sterling (£). Determine:(a) the market equilibrium quantity (Q0) and price (P0)
The quantity demanded of a certain model of a VCR is 8000 units when the unit price is $260. As the unit price decreases by $3, the number of VCRs demanded increases by 100 units. The manufacturer will not market any VCRs if the price is $100 or lower. However, for each $50 increase in the unit price above $100, the manufacturer will market an additional 1000 units. Demand: (8000, 260), (8100, 257) Provide the equations for the linear demand and supply functions: Also, define the variables. D(x) is the price the consumer is willing to spend when purchasing x number of VCRs. S(x) is the price the manufacture is willing to sell x number of VCRs Answer: D(x) = (-3/100)X + 500 and S(x) = (5/100)X + 100
A company participating in a market of perfect competition invoices monthly 154,200 units, the sum of $308,400,000, so P = $2,000 With this level of sales, the company has saturated its production capacity and as a result its costs have risen sharply. Its marginal cost (MC) is MC = (q2 / 2,000,000) - (q / 20) + 2,450. It is determined that its fixed costs (FC) amount to $20,500,000. You want to know: (a) whether the company should increase or decrease its production and by how much. b) what would be the optimal level of production (q*)? c) what is the profit at the optimal level of production? d) what is the company's current profit? PD: I have republished this exercise ONLY to get an answer to question d). Thank you
Supply and Demand The supply function for aproduct is given by p = q3 + 800q + 6000 and thedemand function for this product is p = 12,200 -10q - q2, where p is the price in dollars and q is thenumber of hundreds of units. Find the price that givesmarket equilibrium and the equilibrium quantity
The weekly demand and supply functions for Sportsman 5 ✕ 7 tents are given by p = −0.1x2 − x + 90 and p = 0.1x2 + 2x + 70 respectively, where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity (in hundred units). hundred units Find the equilibrium price (in dollars). $