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scenario: In the town of Isoville there are two grocery stores: Alfonso’s Ammenities and Bernice’s Bargains. The grocery stores are located at either end of the town, 1km apart. Recently, the manager of Alfonso’s Ammenities has proposed installing new self-service checkout technology, which promises to reduce the cost of each transaction at the grocery store by reducing staffing costs. The new technology is expected to reduce the marginal cost of selling a typical basket of groceries by $3. However, experience in other locations has shown that in about 25% of installations the self-service technology results in a significant increase in shop-lifting. In these cases, the need to hire extra security staff means that the marginal cost of a typical basket only falls by $1.50. Unfortunately, there is no way to know whether extra security will be required until after the new checkouts are installed. The market: Isoville has 12,000 households, each of which purchases 1 basket of groceries per week. The households are evenly spaced across the town and they each suffer a disutility of $4 for each kilometre they travel to reach a grocery store. The marginal cost of selling a basket of groceries is currently $15 for each store. At present, the equilibrium price a basket of groceries is $19, and each store has a profit of $24,000 per week. This market is best modelled as Hotelling competition. You should neglect fixed costs in your analysis. (Assume that the fixed costs are the same for both types of checkout technology.) Note: For the purposes of these questions you should treat competition in this market as a one-shot game. Do not consider repetition or associated phenomena such as collusion or predatory pricing. please answer the following questioning considering the information given: Step 1: Derive an expression for the location of the indifferent consumer. Use PA to represent the price of admission at Alfonso’s Ammenities, and PB to represent the price of admission at Bernice’s Bargains Step 2: Find the profit function for Bernice’s Bargains. You should assume that Bernice’s marginal cost is $15. Step 3: Find Bernice’s best-response function. Step 4: Find the profit function for Alfonso’s Ammenities for the case in which their marginal cost is $12.
Akash M.
Arrowmark Vending has the contract to supply pizza at all home football games for a university in the Big 12 athletic conference. It is a constant challenge at each game to determine how many pizzas to have available at the games. Tom Kealey, operations manager for Arrowmark, has determined that his fixed cost of providing pizzas, whether he sells 1 pizza or 4,000 pizzas, is $1,000. This cost includes hiring employees to work at the concession booths, hiring extra employees to cook the pizzas the day of the game, delivering them to the game, and advertising during the game. He believes that this cost should be equally allocated between two types of pizzas. Tom has determined that he will supply only two types of pizzas: plain cheese and pepperoni-and-cheese combo. His cost to make a plain cheese pizza is $4.50 each, and his cost to make a pepperoni-and-cheese combo is $5.00 each. Both pizzas will sell for $9.00 at the game. Unsold pizzas have no value and are donated to a local shelter for the homeless. Experience has shown the following demand distributions for the two types of pizza at home games: Plain Cheese Demand | Probability 200 | 0.10 300 | 0.15 400 | 0.15 500 | 0.20 600 | 0.20 700 | 0.10 800 | 0.05 900 | 0.05 Pepperoni-and-Cheese Demand | Probability 300 | 0.10 400 | 0.20 500 | 0.25 600 | 0.25 700 | 0.15 800 | 0.05 Required Tasks: 1. For each type of pizza, determine the profit (or loss) associated with producing at each possible demand level. For instance, determine the profit if 200 plain cheese pizzas are produced and 200 are demanded. What is the profit if 200 plain cheese pizzas are produced but 300 were demanded, and so on? 2. Compute the expected profit associated with each possible production level (assuming Tom will produce at only one of the possible demand levels) for each type of pizza. 3. Prepare a short report that provides Tom with the information regarding how many of each type of pizza he should produce if he wants to achieve the highest expected profit from pizza sales at the game.
Sri K.
Senior management at Humber bakery requested a new analysis based on adjusting the selling price and the number of units produced under each production plan. Initial probability estimates are also updated. Resulting gross profits ($) and state of nature probabilities are given in the following payoff table. Low Demand Medium Demand High Demand Light Production 55,550 85,000 85,000 Moderate Production 43,100 102,000 102,000 Heavy Production 5,750 64,650 123,550 Probability 0.2 0.5 0.3 a) [8 marks] What is the optimal decision using the minimax regret approach? Show your work. The new analysis also necessitated updating the offer made to Bramptinos under the heavy production plan. The probability that Bramptinos will accept the new offer is 26% and the associated gross profit is determined to be $112,500. Again here, if Bramptinos declines the offer, the loaves will still sell based on current demand conditions (low, medium, or high). b) [8 marks] Using the decision tree you selected from Part B along with the payoffs and probabilities provided in this section, construct a decision tree for the problem. (You can draw manually or use software. Marks will be given for presentation). What is the optimal decision in this case? Why? Before making a final decision on the production plan to adopt, the bakery's manager decides to contact Professor Leung in the Math Department to conduct a market research survey. The results of the survey will indicate either favourable or unfavourable market conditions for premium breads. In the past, when there was Low Demand, Professor Leung's predictions were unfavorable 80% of the time. The professor's predictions have also been favourable given Medium Demand 88% of the time, and unfavourable given High Demand 10% of the time. c) [12 marks] Calculate posterior (revised) probabilities (Round to 3 decimal places; do not round intermediate results). Show calculations or tables. d) [25 marks] Construct a multistage decision tree (based on part b) with the additional information from Professor Leung. e) [2 marks] What is the value of the sample information (EVSI) provided by Professor Leung? f) [3 marks] State the optimal decision strategy if Professor Leung's consulting fees were $500. g) [2 marks] Does the strategy change if Professor Leung's consulting fees were $1500? If yes, state the new optimal strategy? If no, explain.
Dominador T.
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