Question 1

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. Figure from the original question paper What is the sales in HCU 3?\ **NOTE:** Enter your answer to the nearest integer.