Math Answers

If exactly one number in a set of data is changed, will this necessarily change the

median of the set? Explain.

5. Suppose you plan to set up a firm to retail a certain product A. From a market survey, you estimate that the annual sales volume is 20,000 units at a selling price of $25 per unit. You can purchase product A from a manufacturer at a cost of $13 per unit. Total fixed cost, which includes rental, depreciation, etc. is estimated at $180,000 per annum.

(a) Calculate the break-even point in units, in dollars.

(b) Calculate the profit based on the expected sales volume.

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= 𝟗𝒕^𝟐 + 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.

A certain radioactive material is decaying at a rate proportional to the amount present.

If a sample of 50 grams of the material was present initially and after 2 hours the sample lost 10% of its mass, find:

(a) An expression for the mass of the material remaining at any time t.

(b) The mass of the material after 4 hours.

(c) The time at which the material has decayed to one half of its initial mass.

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

You are given the following information on events A, B, C, and D.

P(A) = .4 P(A ∪ D) = .6 P(A ∩ C) = .04

P(B) = .2 P(A⏐B) = .3 P(A ∩ D) = .03

P(C) = .1

a. Compute P(D).

b. Compute P(A ∩ B).

c. Compute P(A⏐C).

d. Compute the probability of the complement of C.

e. Are A and B mutually exclusive? Explain your answer.

f. Are A and B independent? Explain your answer.

g. Are A and C mutually exclusive? Explain your answer.

h. Are A and C independent? Explain your answer.

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)