Business Analytics End Term: 3 April 2022 (January 2022 term)

Suppose you conduct a chi-squared test of independence on the categorical variables cities and brand preferences at the significance level of 0.05. You obtain a p-value of 0.03. What will you conclude?

You have estimated the demand to follow the following relationship: D(p)= 100−5*p. Now, you intend to maximize the revenue R(p) = D(p) *p. You find the first derivative of R(p) with respect to p, equate it to 0 and find p*. What is the value of p*?
NOTE: Enter your answer in one decimal place.

There are 6 business units. There are two outputs and one input under consideration. You are solving the optimization problem for business unit 3 and find that the efficiency is 0.7. You find that the dual variables corresponding to the constraints of business units 4 and 5 are non-zero and the dual variables corresponding to the constraints of other units are zero. The dual variables corresponding to the constraints of business units 4 and 5 are 0.3 and 0.4 respectively. You are given the following table where sales and number of leads are the two outputs.

What is the sales in HCU 3?
NOTE: Enter your answer to the nearest integer.