In: Advanced Math

One of the luxury car manufacturers usually wants to make a limited number of automobiles in a given year and the company’s aim is to expand their profit margins in each car sold. After doing the analysis on the sales of their cars, the company determined the below supply and demand functions of the cars sold:

Supply function: P = 1000 + Q^2

Demand function: P = 21000 – Q^2

a) Calculate the producer, consumer and total surplus at the market equilibrium.

b) If the manufacturer restricts the number of cars manufactured and sold to 800 at the demand price of $15,000, how much is the total producer surplus?

c) A manufacturer wants to maximize the producer surplus and hence determine the quantity (give the whole number) at which this can be possible. Also determine the producer surplus at this quantity.

Building of its reputation for manufacturing no-thrills,
efficient and affordable automobiles, the Indian car manufacturers
Indy Car Limited, is ready to launch an international marketing
campaign, specifically targeting low- to- medium income customers
in Asia and Europe. In preparation for the expected demand
increase, a new production facility will be added in the state of
Andhra Pradesh near Hyderabad to complement the already existing
plants in Mumbai and New Delhi. The Company’s CFO, Raja Jain is
planning to raise the...

Tim Smith is shopping for a used luxury car. He has found one
priced at $ 27000.
The dealer has told Tim that if he can come up with a down
payment of $5 600, the dealer will finance the balance of the
price at a 7% annual rate over 3 years (36 months).
(Hint: Use four decimal places for the monthly interest rate in
all your calculations.)
a. Assuming that Tim accepts the dealer's offer, what will his
monthly...

Major car manufacturers make use of computer simulations to
experiment with possible plant layouts. The simulations are
designed to reflect stochastic effects such as different demand
patterns, chance variations in processing times and breakdowns.
Hence the results of running a simulation to calculate shifts’
production rates need to be analysed using appropriate statistical
methods. Often these computer simulations are quite complex with
quite long runtimes, and hence there is an interest in using as few
runs of the simulation as...

Belinda wants to buy a second-hand car and visits a number of
car dealers before deciding to purchase an as new 1998 Ford Mustang
from American Car Sales. The sales person, Jaxson, tells Belinda
that the car was manufactured in 1998 and had only done 54,000
kms.
Three months later, Belinda has the Mustang serviced with her
local mechanic who was a Mustang enthusiast. He comments on the
fact that the car was in pretty good condition for a 1994...

Belinda wants to buy a second-hand car and visits a number of
car dealers before deciding to purchase an as new 1998 Ford Mustang
from American Car Sales. The sales person, Jaxson, tells Belinda
that the car was manufactured in 1998 and had only done 54,000
kms.
Three months later, Belinda has the Mustang serviced with her
local mechanic who was a Mustang enthusiast. He comments on the
fact that the car was in pretty good condition for a 1994...

.Belinda wants to buy a second-hand car and visits a number of
car dealers before deciding to purchase an as new 1998 Ford Mustang
from American Car Sales. The sales person, Jaxson, tells Belinda
that the car was manufactured in 1998 and had only done 54,000 kms.
Three months later, Belinda has the Mustang serviced with her local
mechanic who was a Mustang enthusiast. He comments on the fact that
the car was in pretty good condition for a 1994...

.Belinda wants to buy a second-hand car and visits a number of
car dealers before deciding to purchase an as new 1998 Ford Mustang
from American Car Sales. The sales person, Jaxson, tells Belinda
that the car was manufactured in 1998 and had only done 54,000
kms.
Three months later, Belinda has the Mustang serviced with her
local mechanic who was a Mustang enthusiast. He comments on the
fact that the car was in pretty good condition for a 1994...

Question 1 [25]
Namibia Car Dealers wants to determine the number of defects per
new car. Suppose you are asked to conduct the quality survey for
cars, suppose you sampled 30 new cars and following data on number
of defects per car were recorded.
0 1 1 2 1 0 2 3 2 1 0 4 3 1 1 0 2 0 0 2 3 0 2 0 2 0 3 1 0 2 a)
Compute the sample mean number...

"Ms. Jones wants to buy a new car for $30,000. She will make a
down payment of $15,000. She would like to borrow the remainder
from a bank at an interest rate of 9.6% compounded monthly. She
agrees to pay off the loan monthly for a period of 3.25 years.
Assume that Ms. Jones has made 16 payments and wants to figure out
the balance remaining immediately after the 16th payment. Determine
the remaining balance."
Show all work

A sports analyst wants to determine if the number of free throws
basketball players make in their second year is more than the
number of free throws they make in their rookie year. To do this,
he selects several random players and compares the average number
of free throws they made per game in their second year of playing
basketball to the average number of free throws they made per game
in their rookie year. Find the test statistic and...

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