# Allen County Community College Marginal Profit Calculus Worksheet

• February 02, 2022/

## 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.