# Allen County Community College Marginal Profit Calculus Worksheet

- February 02, 2022/ Homework Tutors

###
Description

## 10)

## 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 305 at a price of 14 per toaster
- a weekly demand of 197 at a price of 17 per toaster

The financial department estimates that weekly fixed costs will be $1,437 and variable costs (cost per unit) will be $5.

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 262 toasters per week. Round to the nearest cent.

_______$ per toaster

## (11- 14) Break-Even Analysis

$x$ |
$p$
($) |
$C$
($) |

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 |

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

## Use this data to find a linear regression equation for price-demand data, using x as the independent variable: p= ax+b,

## Use this data to find a linear regression model for the cost data, using x as the independent variable: c(x)=cx+d

where c is rounded to the nearest integer and d is rounded to the nearest 10,000.

Use these linear regression models to answer questions 11-14 below.

Use the linear regression models above to answer this question.

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

$ __________

Use the linear regression models above to answer this question.

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

$ ________ per treadmill produced

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

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