Allen County Community College Marginal Profit Calculus Worksheet

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