Question

Assignment 1

Q.1) Fresh Food has recently carried out a survey of the demand for their seasonal fruits. They observed the following

outcomes over the last seven months:

Quantity

Sold Price Advertising

8500 $ 2 $ 2,800

4700 $ 5 $ 200

5800 $ 3 $ 400

7400 $ 2 $ 500

6200 $ 5 $ 3,200

7300 $ 3 $ 1,800

5600 $ 4 $ 900

Regression (Equation)

QSold = 8536.213882 - 835.7223514 Price + 0.592228496 Advertising

A. Estimate sales when the price is $50 and advertising is $100,000, stating any assumption that you need to make.

B. If the firm charges $50 and cost per unit is $30 but increases advertising to $110,000, what conclusions can you derive

in terms of revenues and profits?

Answer 1

The given regression equation is$QSold = 8536.213882 - 835.7223514 Price + 0.592228496 Advertising$

Here Sales is the dependent variable

Price and Advertising are two independent variables

A). when the price is $50 and advertising is $100,000, then the estimated sales is obtained by using regression equation.

$Q Sold = 8536.213882 - 835.7223514 Price + 0.592228496 Advertising$

      $= 8536.213882 - 835.7223514× 50 + 0.592228496× 100000$

    $= 8536.213882 - 41786.11757+ 59222.84960\\ = 25972.94591$

In a multiple linear regression the assumptions are

1. There is a linear relationship between the dependent and independent variables

2. No multi collinearity among independent variables

3. The independent variables are not highly correlated with each other.

4. The variables follows multivariate normal distribution

(B). If the firm charges $50 and advertising to $110,000 then the total quantity sold is 

$Q Sold = 8536.213882 - 835.7223514 Price + 0.592228496 Advertising$

    $= 8536.213882 - 835.7223514× 50 + 0.592228496× 110000$

  $= 8536.213882 - 41786.11757+ 65145.13456 = 31895.23087$

Each item charged $50.

$\therefore, total \space revenue = Quantity\space sold × Price$

                                     $= 31895.23087 ×50$

                                  $= \$1594761.544$

Cost per item is $30.

$\therefore, Total \space cost\space of\space production = Quantity\space sold × Cost$

                                      $= 31895.23087 ×30\\ = \$956856.9261$

Total profit = Total revenue - Production cost - Advertising cost

$= 31895.23087 ×30$

                                       $= \$956856.9261$

Advertising Cost is $110000

Total profit = Total revenue - Production cost - Advertising cost

        $= \$1594761.544 - \$956856.9261 - \$110000\\ = \$527904.6179$