Suppose a company is developing a new smartphone and they want to determine the optimal combination of features to include in their product. They decide to conduct a conjoint analysis to gather data on how consumers value different attributes. They identify three attributes: screen size, battery life, and camera quality. They will test two levels for each attribute: large and small screen size, long and short battery life, and high and low camera quality. The company recruits 200 participants for their study and presents them with six different smartphone profiles to evaluate. The results are as follows:

• Profile 1: Large screen, long battery life, high camera quality - preferred by 40 participants
• Profile 2: Large screen, long battery life, low camera quality - preferred by 20 participants
• Profile 3: Large screen, short battery life, high camera quality - preferred by 30 participants
• Profile 4: Large screen, short battery life, low camera quality - preferred by 15 participants
• Profile 5: Small screen, long battery life, high camera quality - preferred by 25 participants
• Profile 6: Small screen, long battery life, low camera quality - preferred by 70 participants

a) Create a part-worth utility table for the three attributes based on the data collected.

b) Calculate the total utility for each profile and rank them in order of preference.

c) Calculate the range of part-worth utilities and importance weights for each attribute.

d) Using the results from part a) and c), determine the ideal combination of attributes for the company's new smartphone.

(Note: Assume that the part-worth utilities are linear and that the part-worth utility for the lowest level of each attribute is 0.)