The problem statement for this HW: You are producing beverage mugs and are trying to identify the best price-feature-vector. Assume the following attributes and attribute levels: Price: $30, $10, $5 Time Insulated: 0.5 hrs, 1 hrs, 3 hrs Capacity: 12 oz, 20 oz, 32 oz Cleanability: Difficult (7 min), Fair (5 min), Easy (2 min) Containment: Slosh resistant, Spill resistant, Leak resistant Brand: A, B, C Assume the following as the "proposed market scenario", ie the scenario with the current competitors and our proposed candidate. Incumbents 1: $30, 3 hrs, 20 oz, Clean Easy, Leak Resistant, Brand A 2: $10, 1 hrs, 20 oz, Clean Fair, Spill Resistant, Brand B Our proposed candidate 3: $ 30, 1 hrs, 20 oz, Clean Easy, Leak Resistant, Brand C Assume the following cost structure: Time Insulated: 0.5 hrs costs $0.5, 1 hrs costs $1, 3 hrs costs $3 Capacity: 12 oz costs $1.00, 20 oz costs $2.6, 32 oz costs $2.8 Cleanability: Difficult (7 min) costs $1, Fair (5 min) costs $2.2, Easy (2 min) costs $3.0 Containment: Slosh resistant costs $0.5, Spill resistant costs $0.8, Leak resistant costs $1 You are given data on the preference parameters of 311 consumers in this file: mugs- preference-parameters-full.xlsx. The CSV version of this file is here: mugs-preferenceparameters-full.csv Questions: 1. Using the compensatory rule with logit adjustment: Compute and report our candidate's share, cost, margin and expected profit per person under the "proposed market scenario" given above. This question is a strict subset of the next question. If you have done the next question successfully, then all you need to do for this question is report the numbers for Product Candidate 45 which corresponds to our proposed candidate in the "proposed market scenario" given above. Even though this question is a strict subset of the next question, I am asking for it separately. This is because not all students may be able to do the next question successfully as it is a larger and more general computation. Hint to check your answer: The number you should get for expected profit per person is between 4 and 4.5. 2. Discrete Optimization: Consider each of the three levels for each of the five attributes and enumerate all the possibilities in lexical order with Price as the leftmost attribute changing slowest and taking levels sequentially $30, $10, $5, then Time Insulated as the left-second-most attribute changing second-slowest and taking values sequentially 0.5 hrs, 1 hrs, 3 hrs and so on. You will have 243 product candidates. (The lexical order produces indices as shown in this file. Please make sure you list your products in that exact same order. The lexical order of products is obtained by looping as shown in the following R code, which has close similarity in python: mugs-products-lexical-order-loop.R.) Again using the compensatory rule, compute and report the following four columns of numbers for each candidate: the share, the cost,the margin and the expected profit per person (all under the current competition incumbents). The table that you submit needs to have all 243 rows. Hint to check your answer: product candidate 230 has a negative expected profit per customer of between -1.75 and -1.85, and product candidate 106 has an expected profit per customer of between 0.7 and 0.8 . 3. Using the 243-row table you produced in the previous step: Identify the product with the highest expected profit per person. For this optimal product, list the values of the five attributes and its share, cost , margin and expected profit per person. 4. According to the pure algorithmic analytical approach, the best product is the one with the highest expected profit per person (abbreviated here as "EPPP"). However, depending on the objectives of the company, your product manager boss may not agree that this is the best product. He/she may argue you need to consider, as primary criterion, one or more of the remaining three metrics: Share or Cost or Margin or Revenue. 1. What would be the business rationale to launch the product with the highest market share (instead of the product with the highest EPPP)? Respond in 1- 5 sentences. In the 243-row table, identify the product with the highest market share and give the values of the five attributes. To answer this question it may help to plot the 243 products on EPPP versus share like is shown on Product-Price Optimization Slide 19. 2. What would be the business rationale to launch the product with the highest margin (instead of the product with the highest EPPP)? Respond in 1-5 sentences. In the 243-row table, identify the product(s) with the highest margin and give the values of the five attributes. 3. What would be the business rationale to launch the product with the lowest cost (instead of the product with the highest EPPP)? Respond in 1-5 sentences. In the 243-row table, identify the product(s) with the lowest cost and give the values of the five attributes. 4. What would be the business rationale to launch the product with the highest revenue (instead of the product with the highest EPPP)? Respond in 1-5 sentences. In the 243-row table, identify the product(s) with the lowest cost and give the values of the five attributes. Note that revenue is equivalent to sales volume in currency units (which is dollars in this exercise).