Pam has a monthly budget of £120 to be spent on T-shirts and trainers. She could afford to buy two T-shirts and two pairs of trainers. She could also buy eight T-shirts. In each case, she would be spending her entire monthly allowance. 

a) Calculate the price of a T-shirt and the price of a pair of trainers. Write down Pam’s budget equation and draw the corresponding budget line. Mark the two consumption bundles mentioned above. In your graph, clearly label the axes, the budget line, and calculate the coordinates of the points of intersection of the budget line with each axis. Interpret each of those points. 

b) Discuss how Pam’s budget set would change if the price of a T-shirt doubles. Show the relevant changes graphically. How should Pam’s income change so that she could still afford to buy two T-shirts and two pairs of trainers? 

c) Discuss how Pam’s budget constraint would change if the government imposed a tax of £3 per each pair of trainers.

Consider the data in above Table. The target variable is salary. Start by discretizing salary as follows: Less than $35,000 Level 1 $35,000 to less than $45,000 Level 2 $45,000 to less than $55,000 Level 3 Above $55,000 Level 4 5. Construct a classification and regression tree to classify salary based on the other variables. Do as much as you can by hand, before turning to the software. 6. Construct a C4.5 decision tree to classify salary based on the other variables. Do as much as you can by hand, before turning to the software. 7. Compare the two decision trees and discuss the benefits and drawbacks of each. 8. Generate the full set of decision rules for the CART decision tree. 9. Generate the full set of decision rules for the C4.5 decision tree. 10. Compare the two sets of decision rules and discuss the benefits and drawbacks of each. Occupation Gender Age Salary Service Female 45 $48,000 Male 25 $25,000 Male 33 $35,000 Management Male 25 $45,000 Female 35 $65,000 Male 26 $45,000 Female 45 $70,000 Sales Female 40 $50,000 Male 30 $40,000 Staff Female 50 $40,000 Male 25 $25,000 Consider the data in above Table. The target variable is salary. Start by discretizing salary as follows: Less than $35,000 Level 1 $35,000 to less than $45,000 Level 2 $45,000 to less than $55,000 Level 3 Above $55,000 Level 4