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Your firm has recently started to give economic advice to your clients. Acting as a consultant you have estimated the demand curve of a client’s firm to be
AR = 200 - 8x where AR is average revenue ($) and x is output.
Investigation of the client firm’s cost profile shows that the marginal cost is given by: MC = x2 - 28x + 211 where MC is marginal cost ($). Further investigation has shown that the firm’s cost when no production are $10.
(a) Find equation of total cost.
(b) If total revenue is average revenue multiplied by output, find the equation of total revenue.
(c) Use the methods of differentiation, find the turning point(s) of the firm’s profit curve and say whether these point(s) are maxima or minima.
(d) Determine the level of production to give maximum or minimum profit. Find the profit.
(e) Find the equation of marginal revenue and determine the marginal revenue at output level of 20 units.
5. Suppose you plan to set up a firm to retail a certain product A. From
Your firm has recently started to give economic advice to your clients. Acting as a consultant you have estimated the demand curve of a client’s firm to be
AR = 200 - 8x where AR is average revenue ($) and x is output.
Investigation of the client firm’s cost profile shows that the marginal cost is given by: MC = x2 - 28x + 211 where MC is marginal cost ($). Further investigation has shown that the firm’s cost when no production are $10.
(a) Find equation of total cost.
(b) If total revenue is average revenue multiplied by output, find the equation of total revenue.
(c) Use the methods of differentiation, find the turning point(s) of the firm’s profit curve and say whether these point(s) are maxima or minima.
The marketing department of Spager Ltd estimated that if the selling price of product is set at $15 per unit then the sales will be 50 units per week, while, if the selling price is set at $20 per unit, the sales will be 30 units per week. Assume that the graph of this function is linear. The production department estimates that the variable cost will be $5 per unit and that the fixed cost will be $50 per week, and special cost are estimated as $0.125x2, where x is the quantity of output. All production is sold.
(a) Show that the relationship between price (Pr) and quantity sold (x) , are given by the equation Pr = 27.5 - 0.25x.
(b) Find the revenue function, R.
(c) Find the total cost function (C).
(d) Advise the company on production and pricing policy if it wishes to maximize profits, and find the maximum profit.
A particle is moving along a straight line according to the given equation of motion, where s ft is the directed distance of the particle from the origin at t sec. Find the time when the instantaneous acceleration is zero, and then find the directed distance of the particle from the
a. 𝒔 = (𝟏𝟐𝟓)/ (𝟏𝟔𝒕+𝟑𝟐) − 2/5𝒕𝟓 , t≥𝟎
b. 𝒔= 𝟗𝒕𝟐 + 𝟐 √𝟐𝒕+𝟏, t≥𝟎
A rectangular lot adjacent to a highway is to be enclosed by a fence. If the fencing costs $2.50 per foot
along the highway and $1.5 per foot on the other sides, find the dimensions of the largest lot that can
be fenced off for $720.
f lim f(x) = L1 as x approaches a from the left and lim f(x) = L2 as x approaches a from the right. lim f(x) as x approaches a exists only if L1 = L2. true or false
What is the volume of the largest rectangular parallelepiped which can be inscribed in the ellipsoid x2/9+y2/16+z2/36=1? Show that the answer you get gives you the largest volume.(DO NOT USE LAGRANGE MULTIPLIERS)
1. A manufacturing process costs RM 6500 to set up for one year’s use. If items cost RM 85 each to produce and other costs amount to 3.5 x2, where x is the production in hundreds, find the level of production that will minimize the cost per item over the year. What will the total cost amount to at this level of production?
A container with square base, vertical sides, and open top is to have a volume of 1000 . Find the dimensions of the container with minimum surface area.
A church window consisting of a rectangle topped by a semicircle is to have a perimeter p. Find the radius of the semicircle if the area of the window is to be a maximum.
