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 |
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