The Research and Development Division of the Prog pany has been developing four possible new product li nent must now make a decision as to which of these actually will be produced and at what levels. Theref ions research study has been requested to find ther product mix. bstantial cost is associated with beginning the produc oduct, as given in the first row of the following ta ent's objective is to find the product mix that maxim profit (total net revenue minus start-up costs).
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Customary Pricing
There are various types of pricing strategies followed in the market. They are psychological pricing, odd pricing, free onboard pricing, customary pricing, prestige pricing, dual pricing, ruling pricing, negotiated pricing, mark up pricing, etc. each one can be explained as follows:
Multiple Unit Pricing
“Multiple-unit pricing is a practice where a company offers consumers a lower than unit price if a specified number of units are purchased.”
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- The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.City government has collected the following data on annual sales tax collections and new car registrations: Annual Sales Tax Collections (in millions) 1.0 1.4 1.9 2.0 1.8 2.1 2.3 2.5 New Car Registrations (in millions) 10 12 15 16 14 17 20 22 Determine the following: Plot these data and decide if a linear model is reasonable. Using the results of part a., find the estimated sales tax collections if new car registrations total 25,000,000.Diamond City Amusement Park management is preparing the park's annual promotional plan for the coming season. Several advertising alternatives exist: newspaper, television, radio, and displays at recreational shows. The information below shows the characteristics associated with each of the advertising alternatives, as well as the maximum number of placements available in each medium. Management also wants the total of television and radio placements not to exceed 80. Given an advertising budget of 2,500,000 pesos, how many placements should be made in each medium to maximize total audience exposure? Formulate this as a linear programming problem.
- Problem 8-21 (Algorithmic) Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Rental Class Room Super Saver Deluxe Business Type I $30 $35 — Type II $20 $30 $40 Type I rooms do not have wireless Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be…Mr. R. loves steaks and potatoes. Therefore, he has decided to go on a steady diet of only these two foods (plus some liquids and vitamin supplements) for all his meals. Mr. R. realizes that this is not the healthiest diet, so he wants to make sure that he eats the right quantities of the two foods to satisfy some key nutritional requirements. He has obtained the following nutritional and cost information. Mr. R. wishes to determine the number of daily servings of steak and potatoes that will meet the above daily requirements at a minimum cost. Present this case (a) Algebraically, (b) graphically, and (c) on a spreadsheet then Solve the case using Solver on ExcelDouble Tree Hilton is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Rental Class Super Saver Deluxe Business Room Type I $30 $35 $50 Type II $20 $30 $40 Double Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class.The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 in the Deluxe class, and 50 in the Business class. (These demands are the maximum numbers to accept for each rental class. The actual reservation may be less.) Double Tree has 100 Type I rooms and 130 Type II rooms. 1. Question text How many decision variables are there in your model? What is the maximum profits($)? What is the number of…
- Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rod is $2,000, and the cost required to set up the production for the 6-cylinder connecting rod is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line.Once the line has been set up, the weekly production capacities are 6,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Letx4 = the number of 4-cylinder connecting rods produced next week,x6 = the number of 6-cylinder connecting rods produced next week,s4 = 1 if the production line is set up to produce the 4-cylinder…Type the linear program, optimal solution, and objective function value in a word document. Submit your excel file. An investor wishes to invest some or all of his $12.5 million in a diversified portfolio through a commercial lender. The types of investments, the expected interest per year, and the maximum allowed percentage investment he will consider are shown on the following table. He wants at least 35% of his investments to be in nonmortgage instruments and no more than 60% to be in high-yield (and high-risk) instruments (i.e., expected interest > 8%). How should his investment be diversified to make the most interest income? Investment Expected Return Maximum Allowed Low-income mortgage loans 6.50% 20% Conventional mortgage loans 6.00% 30% Government sponsored mortgage loans 8.25% 25% Bond investments 5.75% 15% Stock investments 8.75% 18% Futures trading 9.25% 10%The following table presents cost, capacity, and demand data for a transportation problem in Stephanie Robbin’s furniture company. Set up the appropriate transportation table and find the optimal solution using Excel's solver. From/To 1 2 3 Supply A 30 10 5 20 B 10 10 10 30 C 20 10 25 75 Demand 40 60 55 a. Is the problem balanced? [ Select ] ["Yes", "it is balanced", "No", "cannot determine"] , If not, where? [ Select ] ["Neither", "Supply", "Demand"] , and by how much? [ Select ] ["0", "40", "30", "25"] b. What is the optimal cost? $ [ Select ] ["2,500", "1,100", "1,275", "1,300"] c. Were you able to meet all demand requirement? [ Select ] ["no", "cannot determine based on the information given", "yes"] If not, which destination (s) was/were not met? [ Select ] ["none, all destinations were met based on supply and demand being equal", "destination 3 by 30 units", "destination 2 by 30 units", "destination 1 by 25 units…
- Rand Enterprises is considering a number of investment possibilities. Specifically, each investment under consideration will draw on the capital account during each of its first three years, but in the long run, each is predicted to achieve a positive net present value (NPV). Listed here are the investment alternatives, their net present values, and their capital requirements, and all figures are in millions of dollars. In addition, the amount of capital available to the investments in each of the next three years is predicted to be $20 million, $12 million, and $20 million, respectively. Project One-PhaseExpansion Two-PhaseExpansion TestMarket AdvertisingCampaign BasicResearch PurchaseEquipment NPV 5.0 8.1 11.6 5.3 10.4 4.2 Year 1 Capital 3.6 3.0 7.2 2.4 6.0 1.2 Year 2 Capital 1.2 4.2 4.8 1.8 1.2 0.6 Year 3 Capital 4.8 4.2 6.0 2.2 4.8 1.1 In addition, the following constraints have to be met: a. The expansion investments are mutually exclusive and only one of…A local television station plans to drop three Friday evening programs at the end of the season. Steve Botuchis, the station manager, developed a list of three potential replacement programs. Estimates of the advertising revenue (in dollars) that can be expected for each of the new programs in the three vacated time slots are as in Table 3. Table 3: Problem 1.9 5-6 PM 6-7 PM 7-8 PMHome Improvement 5000 3000 6000World News 7500 8000 7000Hollywood Briefings 7000 8000 3000 Mr. Botuchis asked you to find the assignment of programs to time slots that will maximize total advertising revenue. list constraints and explain.A local television station plans to drop three Friday evening programs at the end of the season. Steve Botuchis, the station manager, developed a list of three potential replacement programs. Estimates of the advertising revenue (in dollars) that can be expected for each of the new programs in the three vacated time slots are as in Table 3. Table 3: Problem 1.9 5-6 PM 6-7 PM 7-8 PMHome Improvement 5000 3000 6000World News 7500 8000 7000Hollywood Briefings 7000 8000 3000 Mr. Botuchis asked you to find the assignment of programs to time slots that will maximize total advertising revenue.