Question 1: A waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 21y * d ^ 3 of debris. Find the dimensions of the dumpster that will minimize its surface area.

Write the surface area formula in terms of the widthAssume the dumpster has an open top SA =

The The width of the dumpster is blank and blan the length of the dumpster blank and blank is the highest of the dumpster is blank and blank (Round to the nearest hundredth as needed.

Question 2

Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per suit must be p

=1700.75x. It also determines that the total cost of producing x suits is given by

C(x)=4000+0.5x2.

a) Find the total revenue,R(x).

b) Find the total profit,P(x).

c) How many suits must the company produce and sell in order to maximize profit?

d) What is the maximum profit?

e) What price per suit must be charged in order to maximize profit?

Qustion 3

For the demand function q=D(p)=Square root 351 p, find the following.

a) The elasticity

b) The elasticity at p= 99, stating whether the demand is elastic, inelastic or has unit elasticity

c) The value(s) of p for which total revenue is a maximum (assume that p is in dollars)

Part 1

a) Find the equation for elasticity.

E(p) =

b) Find the elasticity at the given price, stating whether the demand is elastic, inelastic or has unit elasticity.E(99)=

(Simplify your answer. Type an integer or a fraction.)

Part 3

Is the demand elastic, inelastic, or does it have unit elasticity?

inelastic

elastic

unit elasticity

Part 4

c) Find the value(s) of p for which total revenue is a maximum (assume that p is in dollars).

$

enter your response here

(Round to the nearest cent. Use a comma to separate answers as needed.)

Question 4

Find the equation(s) of the tangent line(s) to the graph of the indicated equation at the point(s) with the given value of x.

xyx16=0; x=2

Find the equation(s) of the tangent line(s) to the graph of the given equation at x=2.

(Type an equation. Use a comma to separate answers as needed.)

Question 5

Find the absolute extrema if they exist, as well as all values of x where they occur, for the function

f(x) =5x/1+x

on the domain[0,1].

Find the derivative of f(x)=5x/1+x

.f(x)=

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A.

The absolute maximum is blank , which occurs at x=. Blank

(Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.)

B.

There is no absolute maximum.

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A.

The absolute minimum is blank , which occurs at x= blank

.(Round the absolute minimum to two decimal places as needed. Type an exact answer for the value of x where the minimum occurs. Use a comma to separate answers as needed.)

B.

There is no absolute minimum