A firm has monthly average costs, in dollars, given by

C =

+ 200 + x

where x is the number of units produced per month. The firm can sell its product in a competitive market for $1800 per unit. If production is limited to 400 units per month, find the number of units that gives maximum profit.
x =  units

Find the maximum profit.
$  

Please answer all 3 questions and explain . thank you.

(1) Determine the length of the curve y= 3 + 2x^(3/2) for 0 ≤ x ≤ 2. You can use your calculator at the last step (after the integration) to determine the approximate length, or you may keep it exact.

(2) Set up, but do not evaluate an integral for the surface area obtained by rotating the curve y = x^3+ 4, 1 ≤ x ≤ 5 (a) about the x-axis. (b)about the y-axis.

(3)Find the particular solution to the differential equation dy dx = y 2 sin x that satisfies the initial condition y(0) = 3.

F(x)=g(x)*h(x) = 4x³-2x²+3x-1 solution

Use a triple integral to find the volume of the solid enclosed by the paraboloids y= x²+z² and y= x²+z²

The demand for nurses in the US between 2000 and 2015 is estimated to be D(t) = 0.7t 2 + 0.265t + 2000 thousand, where 0 ≤ t ≤ 15, and t = 0 corresponds to year 2000. The number of nurses in the US between 2000 and 2015 is estimated to be S(t) = 0.14t 2 + 0.326t + 1900 thousand, where 0 ≤ t ≤ 15, and t = 0 corresponds to year 2000.

In the marginal analysis, you would use q'(8) to estimate what quantity? Find the exact value of that quantity, and compare with q' (8).

If all proper nontrivial subgroups of a nontrivial group are isomorphic to each other, must G be cyclic?

1. Find absolute max and min of     f(x,y)= x^2- xy + y^2 +1 on the closed triangular plate in the first quadrant x=0, y=4, y=x

2. Given position of a particle by π (t)= Cos2ti + 3 sin2ti,         Find the particle velocity and acceleration at t=0

1. a) Based on recent statistics, Green Way Airlines expects 4.2% of its customers will be “no shows”. If the airline sold 260 seats for a flight, how many people would the airline expect as “no-shows”? (Round to the nearest whole number)

b) If the airplane can hold 254 passengers, can all those who show up at the gate get on the plane? Explain

2. JK Builders bought 35 acres of land for a housing development. They will give 1.75 acres to the city for a playground and subdivide the remaining land into house lots of 0.875 acres. How many house lots can be formed?    

3. The average snowfall amounts for 5 winter months in Burlington, Vermont are given in the table.

    a) Find the mean snowfall amount.   

   b) Find the median snowfall amount.                                                                                                             

4. Volunteers from Habitat for Humanity are painting 16 interior walls in new homes that have been built. Each wall measures 14 feet by 6 2/3 feet.

a) If a gallon of paint covers 400 square feet, how many gallons will be required to paint all the walls? (Round to next whole number)

b) If each gallon costs $27.95, find the cost of the project.

5. In a recent year, wind machines in the United States generated 17.8 billion kilowatt-hours of electricity (enough to power more than 1.6 million households). The nation’s total electricity production was 4450 billion kilowatt-hours. What percent of the total electrical energy production was generated by wind machines?

6. If a 5 1/4 inch line on a map represents a 9-mile road, how many miles would be represented by a 3 1/2 inch line?

7. At a fire sale, items are being sold at 3/4 off the marked price. What is the sale price of an item that has a marked price of $156?

8. Sixteen ounces of mouthwash costs $3.49 while a 33-ounce container of the same brand costs $6.99. Which is a better buy? Why?

9. The price of gasoline jumped from $3.24 per gallon to $4.05 per gallon in one year. What was the percent increase?

10. You buy 2.75 yards of material at $4.80 per yard and pay $0.87 sales tax. What is the total cost for your purchase?

11. Ruth orders clothes from a retail catalog. She orders two turtleneck tops for $35 each, two pairs of stretch pants for $45 each, one winter jacket for $130, and three leather belts for $25 each. The shipping and handling charge for the order is $15. What is the total charge for Ruth’s order?

12. A recipe for a wedding punch calls for 12 quarts of champagne. If the champagne comes in bottles that are 4/5 of a quart, how many bottles of champagne would be needed?

13. One bank offers a 4-year car loan at an annual simple interest rate of 7% plus a loan application fee of $45. A second bank offers 4-year car loans at an annual simple interest rate of 8% but no loan application fee. If you need to borrow $5800 to purchase a car, which of the two bank loans has the lesser loan cost? (Assume you keep the car for all 4 years.)

14. In a recent survey of new car buyers, 20 of 63 men said they would prefer to buy a silver car while 16 of 49 women said they would prefer silver.

a) Which group has a stronger preference for silver cars?

b) Explain your answer

15. How many acres are contained in 1 square mile? (1 mile = 5280 ft.; 1 acre = 43,560 sq. ft.)

A patient's pulse measures 150 bpm, 80 bpm, then 100 bpm. To determine an accurate measurement of pulse, the doctor wants to know what value minimizes the expression

(x − 150)² + (x − 80)² + (x − 100)².

What value (in bpm) minimizes it?

_________bpm

The total weekly revenue earned at Royal Ruby Retailers is given by

R(p) = −7/3p² + 98p

where p is the price (in dollars) RRR charges per ruby. Use this function to determine the following.

(a) Determine the weekly revenue, to the nearest dollar, when the price is set at $20/ruby.
$

(b) Determine the weekly revenue, to the nearest dollar, when the price is set at $200/ruby.
$

Interpret your result.

The range of the demand function cannot realistically include p = $200. The range of the demand function includes p = $200.     The domain of the demand function cannot realistically include p = $200. The domain of the demand function includes p = $200.

(c) Determine the price RRR should charge in order to obtain a weekly revenue of $1,029.

(i) Find the cylinder inscribed in a sphere with radius one with the largest surface area.

1. Using calculus and the SDT (then FDT if necessary), find all global and local maximum

   and minimums given the function ?(?) = ?^3 + ?^2 − ? + 1 where ? ∈ [−2, 1/2]. Clearly

   identify critical values and show the SDT then the FDT if the SDT didn’t provide an answer and then interpret the solution.

A rectangle storage container with an open top should have a volume of 33 meters^3. The length of its base is 2 times the width. Material costs for the base are $10/meter^2 and the material costs for the sides are $22/meter^2. Optimize the costs of materials (hint minimum cost we are not trying to sell it).

For x = ρsinφcosθ; y = ρsinφsinθ; z = ρcosφ:

a/ Express ∂^2/∂y^2 with ρ, φ, θ, and their partials.

b/ Express ∂^2/∂z^2 with ρ, φ, θ, and their partials.

c/ Express the Laplacian operator using spherical coordinates.