Question

The price P per unit at which a company can sell all that it produces is given by the function P(x) = 300 — 4x. The cost function is c(x) = 500 + 28x where x is the number of units produced. Find x so that the profit is maximum.

Answer the following question.

Q1. Find the value of x.

Q2. In using regression analysis for making predictions what are the assumptions involved.

Q3. What is a simple linear regression model?

Q4. What is a scatter diagram method?

Answer 1

1) Profit = Sales - Cost

Sales = Quantity* Price = X(300-4x)
Cost = 500+28x

Profit = (300x-4x^2)-(500+28x)
= -4x^2 + 272x - 500
Profit is maximum when -8x+272=0, or
x = 34

2) We will make five assumptions in using regression:

1. Linear Relationship
2. Multivariate Normality
3. No or little multicollinearity
4. No auto-correlation
5. Homoscedasticity

3) Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables:

• One variable, denoted x, is regarded as the predictor, explanatory, or independent variable.
• The other variable, denoted y, is regarded as the response, outcome, or dependent variable.

4) Scatter graph method is a graphical technique of separating fixed and variable components of mixed cost by plotting activity level along x-axis and corresponding total cost (mixed cost) along y-axis.