?

You notice that annual housing rents decrease by $800 per unit for every mile traveling away from downtown Baltimore in a suburban neighborhood with 0.25 acre lots. Assume that the interest rate is 4 percent, and the city boundary expands at 1 percent. Assume that the lot size and house size are fixed at all locations (i.e., no factor substitution as explained in Chapter 3).

Use your knowledge of Chapter 3 on “The Urban Land Market”.

6a. What is the slope of the housing rent per unit within the city? (5 points)

6b. What is the slope of the land price per acre within the city? (5 points)

6c. Farmland on the edge of the city boundary is selling for a price of $80,000 per acre. How much should you pay for a one acre vacant lot inside the city that is located 2 miles from the city boundary? (10 points)

A nursery operator is considering installing a wireless sensor network that will control irrigation automatically to keep moisture at a preset level. She currently uses 80,000,000 gallons of water a year. The automated irrigation system will cut water use by one-half. The system requires an initial investment of $50,000 and will last 25 years. The nursery operator can finance this investment over a 25-year period at a fixed interest rate of 10%, compounded annually.

a. Calculate the annualized cost of the wireless sensor system.

b. Calculate the present value of the water savings if the nursery operator gets

water from a nearby river that costs $0.00015 per gallon.

c. Will investing in the automated irrigation system be profitable for this

A nursery operator is considering installing a wireless sensor network that will control irrigation automatically to keep moisture at a preset level. She currently uses 80,000,000 gallons of water a year. The automated irrigation system will cut water use by one-half. The system requires an initial investment of $50,000 and will last 25 years. The nursery operator can finance this investment over a 25-year period at a fixed interest rate of 10%, compounded annually.

A new ethanol plant is about to open in a farming area with 10,000 acres of corn divided equally among 10 farms. The new plant is expected to increase profit from corn sales by 10%. By how much (in dollars) will the new ethanol plant increase the price of a farm in this area if profit from corn currently averages $200 per acre and the interest rate is 2%

i just need help with part c and part d

part c says

let r(x)= -x^2+37x+38 denote the revenue in thousands of dollars generated from the production of x units what is the breakeven point (recall that the breakeven point is when revenue is equal to cost)

-i tried setting them equal but did not get the correct answer

part d

comute and compare the marginal revenue and margianl cost at the break even point should the company increaese production beyond breakeven point justify your answer using marginals

thank you for reading over this and helping!

find the number a based on the following information

f(x)= -8x^4

f (a)= -32

A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk 3 miles per hour in the forest and travel 4 miles per hour along the road. In the picture below, the forest ranger walks in a straight line to a point x unit from the end of the road on the left, and then along the road.

The total travel time for the ranger to get to the car is the sum of the travel time in the forest and the travel time on the road. Write the total time T as a function of x, using the letter c for the distance from the end of the road on the left to the car.

Toward what point on the road should the ranger walk in order to minimize the travel time to the car if...

(a) c = 8 miles? (Numerical Answer ONLY)

c = 1/5 miles? Remember that the point must lie between the left end of the highway and the car. (Numerical Answer ONLY)

x =

Think about the case when c is an arbitrary number of miles. Toward what point should the ranger walk in this case?

At 6 P.M. an oil tanker traveling west in the ocean at 20 kilometers per hour passes the same spot as a luxury liner that arrived at the same spot at 5 P.M. while traveling north at 40 kilometers per hour. If the "spot" is represented by the origin, find the location of the oil tanker and the location of the luxury liner t hours after 5 P.M. Then find the distance D between the oil tanker and the luxury liner at that time.

At what time were the ships closest together? (Hint: Minimize the distance (or the square of the distance!) between them.)

The time is ______:____ round to the nearest min

A crate open at the top has vertical sides, a square bottom, and a volume of 864 cubic meters. Using the labels shown in the figure, write the surface area S as a function of x.

If the crate has the least possible surface area, find its dimensions.

x=_____ meters

y=______meters

z=_______meters

s''(x)______ value for your solution for x

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Question: The product of two numbers is 34. Find the sum of the two numbers S(x) as a function of one of th...

The product of two numbers is 34. Find the sum of the two numbers S(x) as a function of one of the numbers, x.

S(x) =

Find the positive numbers that minimize the sum and list them in increasing order:

(smaller number)=?

(larger number)=?

Let c be the smaller of the two numbers that minimize the sum. Then

c =?

S (c) = ? and

S"(c) = ?

A culture contains 1000 bacteria initially and doubles every 30 minutes. Assuming that the rate of growth is proportional to the number of bacteria, find a function that models the number P(t) of bacteria after t minutes.

It is known that a certain kind of algae in the Dead Sea can double in population every 2 days. Suppose that the population of algae grows exponentially, beginning now with a population of 3,000,000.

) How long it will take for the population to quadruple in size?___ days

How long it will take for the population to triple in size?____ days

Suppose an unknown radioactive substance produces 4800 counts per minute on a Geiger counter at a certain time, and only 600 counts per minute 8 days later. Assuming that the amount of radioactive substance is proportional to the number of counts per minute, determine the half-life of the radioactive substance.

The radioactive substance has a half-life of

days.