A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. How many ways are there to choose: (a) 26 candies? Answer = 27405 (b) 26 candies with at least a piece of each flavor? Answer = 12650 (b) 26 candies with at least 1 cherry and at least 4 lemon?
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- When you use a RISKSIMTABLE function for a decision variable, such as the order quantity in the Walton model, explain how this provides a fair comparison across the different values tested.You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
- Suppose that GLC earns a 2000 profit each time a person buys a car. We want to determine how the expected profit earned from a customer depends on the quality of GLCs cars. We assume a typical customer will purchase 10 cars during her lifetime. She will purchase a car now (year 1) and then purchase a car every five yearsduring year 6, year 11, and so on. For simplicity, we assume that Hundo is GLCs only competitor. We also assume that if the consumer is satisfied with the car she purchases, she will buy her next car from the same company, but if she is not satisfied, she will buy her next car from the other company. Hundo produces cars that satisfy 80% of its customers. Currently, GLC produces cars that also satisfy 80% of its customers. Consider a customer whose first car is a GLC car. If profits are discounted at 10% annually, use simulation to estimate the value of this customer to GLC. Also estimate the value of a customer to GLC if it can raise its customer satisfaction rating to 85%, to 90%, or to 95%. You can interpret the satisfaction value as the probability that a customer will not switch companies.Ten different types of brownies are sold. You arethinking of developing a new brownie for sale.Brownies are rated on the basis of five qualities: price,chocolate flavor, chewiness, sweetness, and ease ofpreparation. You want to group the 10 brownies on themarket into three clusters. Each cluster should containbrownies that are relatively similar.a. Why would this be useful to you?b. How would you do it?A company manufactures two products. If it chargesprice pi for product i, it can sell qi units of product i,where q1 = 60 - 3p1 + p2 and q2 = 80 - 2p2 + p1. Itcosts $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of eachproduct should the company produce, and what pricesshould it charge, to maximize its profit? Use spreadsheet modelling in Excel
- LINGO SOFTWARE Consider a production-mix problem where we are concerned with what mix of four products we should produce during the upcoming week. For each product, each unit produced requires a known amount of production time on each of the three machines. Each machine has a certain number of hours of production time available per week. Each product provides a certain profit per unit produced. Figure 3S1.2 shows three types of data: machine-related data, product-related data, and data related to combinations of a machine and product. The objective is to determine how much to produce for each product so that total profit is maximized while not exceeding the limited production capacity of each machine. Requirement: Solve this problem in LINGO software.Struggling with answering this question A manufacturer produces three types of humidifiers. The retail price of Humidifier Regular (HR) is $60 with variable costs of $20. Humidifier Advanced (HA) sells for $200 for its advanced features. This model’s variable costs are $80. Humidifier Simple (HS) is a simplified version and only sells for $25 with variable costs of $15. The manufacturer has machines and facilities worth $320,000 annually. The sales data show that 1000 units of HR, 2000 units of HA, and 10,000 units of HS was sold last year. Calculate the break-even point of the firm. The firm has some idle capacity at these volumes and chooses to cut the selling price of HR from $60 to $45, believing that its sales volume will rise from 1000 units to 2500 units. What is the revised break-even point?A person sells and installs A, B and C. The table shows, for example, that it takes 3 hours to sell a unit of B, it takes 4 hours to install it, and net profit per unit is $ 40. Product No. of Units Selling Hours per Unit Installation Hours per Unit Profit per Unit A x 1 1 $10 B y 3 4 40 C z 2 1 10 During a 38-hour week, the person allots no more than 18 hours to selling and no more than 20 hours to installation. Find the combination of number of units of A, B, C that would yield maximum profit.
- 1. Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you? 2. Suppose that a manager has a choice between the following two mathematical models of a given situation: (a)a relatively simple model that is a reasonable approximation of the real situation, and (b)a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?A buyer for a large department store chain must place orders with an athletic shoe manufacturer six months prior to the time the shoes will be sold in the department stores. The buyer must decide on November 1 how many pairs of the manufacturer's newest model of tennis shoes to order for sale during the coming summer season. Assume that each pair of this new brand of tennis shoes costs the department store chain $65 per pair. Furthermore, assume that each pair of these shoes can then be sold to the chain's customers for $85 per pair. Any pairs of these shoes remaining unsold at the end of the summer season will be sold in a closeout sale next fall for $55 each. The probability distribution of consumer demand for these tennis shoes during the coming summer season has been assessed by market research specialists and is provided in the file P09_35.xlsx. Finally, assume that the department store chain must purchase these tennis shoes from the manufacturer in lots of 100 pairs. a. Identify…A buyer for a large department store chain must place orders with an athletic shoe manufacturer six months prior to the time the shoes will be sold in the department stores. The buyer must decide on November 1 how many pairs of the manufacturer's newest model of tennis shoes to order for sale during the coming summer season. Assume that each pair of this new brand of tennis shoes costs the department store chain $65 per pair. Furthermore, assume that each pair of these shoes can then be sold to the chain's customers for $85 per pair. Any pairs of these shoes remaining unsold at the end of the summer season will be sold in a closeout sale next fall for $55 each. The probability distribution of consumer demand for these tennis shoes during the coming summer season has been assessed by market research specialists and is provided in the file P09_35.xlsx. Finally, assume that the department store chain must purchase these tennis shoes from the manufacturer in lots of 100 pairs. a. Identify…