Sales Analysis

A company's total sales (in millions of dollars)months from now are given by

S(t)=0.03t^3+0.5t^2+2t+3

Use this sales model to answer questions 1-2 below.

1/ What are the predicted total sales 10 months from now? Round to the nearest dollar.

2/ What is the instantaneous rate of change of3 months from now? Round to 2 decimal places.

millions of dollars per month

3/Price-Demand Equation

At YasterMart, people are willing to buy pounds of chocolate candy per day at $dollars per quarter pound, as given by the price-demand equation x= a+b/p, where= 9 and240.

Find the instantaneous rate of change of demand with respect to price when the price is $5.61. Round to the nearest hundredth (2 decimal places)

pounds per dollar

College Enrollment

The percentage of female high school graduates who enrolled in college is given in the table below.

Year	College Enrollment Percentages for Females
1970	25.5
1980	30.3
1990	38.3
2000	45.6
2010	50.5

Let represent time (in years) since 1970, and let represent the corresponding percentage of female high school graduates who enrolled in college.

Find the cubic regression model

, y= F(x)=ax^3+bx^2+cx+d

where is rounded to 6 decimal places,is rounded to 4 decimal places,is rounded to 3 decimal places, and is rounded to 1 decimal place?

Use this cubic regression model to answer questions 4-5 below

4/ Use the cubic regression model above to answer this question.

Predict the percentage of female high school graduates in 2029. Round to the nearest tenth (1 decimal place).

%

5/ Use the cubic regression model above to answer this question.

Predict instantaneous rate of change of the percentage of female high school graduates in 2027. Round to the nearest hundredth (2 decimal places).

% per year

NOTE: Your answer may be negative.

6/ Advertising

Jesaki Inc will sellunits of the product after spending $thousand in advertising, as given by

N= 79x-x^2

Use differential approximations to estimate the increase in sales that will result by increasing the advertising budget from $10,000 to $10,784. Round to the nearest dollar.

$

7/ Average Cost

Jester Sports manufactures tennis rackets. The total cost of producingrackets per hour is given by

0.57x^2 + 4.4x+ 417.

The average cost per racket at production levelx rackets per hour is C(x)=C(x)/x.

Use differential approximations to estimate the change in average cost per racket if the production is increased from 20 per hour to 24 per hour. Round to the nearest cent.

$ per racket

NOTE: Your answer may be negative.

8/ Revenue, Cost, and Profit

Yaster Electronics manufactures and sellstelevisions per month. The cost and revenue in dollars are given byC(x) 74,558 + 58x and R(x) 208- 0.043.

Use differential approximations to estimate the change in profit if production level is increased from 1,500 to 1,568. Round to the nearest dollar.

$

NOTE: Your answer might be negative.

9/ Marginal Profit

Yaster Breakfast Supplies is planning to manufacture and market a new toaster. After conducting extensive market surveys, the research department provides the following estimates:

• a weekly demand of 299 at a price of $15 per toaster
• a weekly demand of 192 at a price of $17 per toaster

The financial department estimates that weekly fixed costs will be $1,386 and variable costs (cost per unit) will be $4.

Assume:

• the relationship between price and demand is linear
• the cost function in linear

Use your models to predict the marginal profit when Yaster is producing and selling 265 toasters per week. Round to the nearest cent.

$ per toaster

Break-Even Analysis

The table below contains price-demand and total cost data for the production of treadmills, where is the wholesale price (in dollars) of a treadmill for an annual demand of treadmills, andis the total cost (in dollars) of producing treadmills.

	($)	($)
2,910	1,450	3,634,000
3,415	1,275	3,782,000
4,645	1,123	4,185,000
5,330	918	4,290,000

Use this data to find a linear regression equation for price-demand data, usingx as the independent variable:

,p=ax+b

where is rounded to 1 decimal place and is rounded to the nearest integer?

Use this data to find a linear regression model for the cost data, usingas the independent variable:

C(x)=Cx+d

where is rounded to the nearest integer and is rounded to the nearest 10,000?

Use these linear regression models to answer questions 10-13 below.

10/ Use the linear regression models above to answer this question.

Estimate the fixed costs. Round to the nearest $10,000.

$

11/ Use the linear regression models above to answer this question.

Estimate the variable cost per treadmill. Round to the nearest dollar.

$ per treadmill produced

12/ Use the linear regression models above to answer this question.

There are two break-even points. Find the smaller production level where the company breaks even. Round to the nearest treadmill.

treadmills

13/ Use the linear regression models above to answer this question.

There are two break-even points. Find the larger production level where the company breaks even. Round to the nearest treadmill.

treadmills