A manufacturer produces both widgets and gadgets. Widgets generate a profit of $45 each and gadgets have a profit margin of $55 each. To produce each item, a setup cost is incurred. This setup cost is $300 for widgets and $600 for gadgets. Widgets consume 4 units of raw material A and 7 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 400 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets. Set up the problem in Excel and find the optimal solution. a. The manufacturer widgets and gadgets.
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- In the lawn mower production problem in Example 8.4, experiment with the penalty cost for unsatisfied pickups in week 1. If this cost is sufficiently small, does the company ever produce fewer than seven models in week 1 and allow some week 1 pickups to be unsatisfied?Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?A manufacturer produces both widgets and gadgets. Widgets generate a profit of $50 each and gadgets have a profit margin of $40 each. To produce each item, a setup cost is incurred. This setup cost is $300 for widgets and $400 for gadgets. Widgets consume 5 units of raw material A and 4 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 600 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets. Set up the problem in Excel and find the optimal solution.
- A manufacturer produces both widgets and gadgets. Widgets generate a profit of $25 each and gadgets have a profit margin of $75 each. To produce each item, a setup cost is incurred. This setup cost is $400 for widgets and $300 for gadgets. Widgets consume 6 units of raw material A and 8 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 400 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets. Set up the problem in Excel and find the optimal solution. The manufacturer will produce .......widgets and ...... gadgets the manufacturer's profit will be ......A manufacturer produces both widgets and gadgets. Widgets generate a profit of $70 each and gadgets have a profit margin of $45 each. To produce each item, a setup cost is incurred. This setup cost is $400 for widgets and $500 for gadgets. Widgets consume 5 units of raw material A and 6 units of raw material B. Gadgets consume 6 units of raw material A and 2 units of raw material B. Each day, the manufacturer has 500 units of each raw material available. Assume that it is possible to produce fractional quantities of widgets and gadgets.Set up the problem in Excel and find the optimal solution. (Leave no cells blank — be certain to enter "0" wherever required. Round your answers to 2 decimal places.) (Round your answer to 2 decimal places.)A glassblower makes glass decanters and glass trays on a weekly basis. Each item requires 1 pound of glass, and the glassblower has 15 pounds of glass available each week. A glass de- canter requires 4 hours of labor, a glass tray requires only 1 hour of labor, and the glassblower works 25 hours a week. The profit from a decanter is $50, and the profit from a tray is $10. The glassblower wants to determine the total number of decanters (x1) and trays (x2) that he needs to produce in order to maximize his profit. Requirements:a) Define decision variables and tabulated datab) Formulate the Integer Linear Programming Model.
- Stan Moneymaker needs 15 gallons of gasoline to top off his automobile’s gas tank. If he drives an extra eight miles (round trip) to a gas station on the outskirts of town, Stan can save $0.10 per gallon on the price of gasoline. Suppose gasoline costs $3.90 per gallon and Stan’s car gets 25 mpg for in-town driving. Should Stan make the trip to get less expensive gasoline? Each mile that Stan drives creates one pound of carbon dioxide. Each pound of CO2 has a cost impact of $0.02 on the environment. What other factors (cost and otherwise) should Stan consider in his decision making?A jeweler and her apprentice make silver pins and necklaces by hand. Each week they have 80 hours of labor and 36 ounces of silver available. It requires 8 hours of labor and 2 ounces of silver to make a pin and 10 hours of labor and 6 ounces of silver to make a necklace. Each pin also contains a small gem of some kind. The demand for pins is no more than six per week. A pin earns the jeweler $400 in profit, and a necklace earns $100. The jeweler wants to know how many of each item to make each week to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer. Compare this solution with the solution without integer restrictions and indicate whether the roundeddown solution would have been optimal.A firm making snowblowers produces the augers for each snowblower in batches. Annual demand is for 3,000 snowblowers, which means 3,000 augers need to be produced each year. On a given workday, 10 augers are needed for snowblower production. Annual holding costs are $3 per auger. Before the augers are produced, a setup cost of $100 is incurred to setup the equipment to produce a batch of augers. The firm can produce 50 augers per day. Given this information, find the economic production quantity for the auger units. Note: When doing interim calculations, round value to 2 decimal points.
- A company produces three types of items. A singlemachine is used to produce the three items on a cyclicalbasis. The company has the policy that every item isproduced once during each cycle, and it wants to determinethe number of production cycles per year that will minimizethe sum of holding and setup costs (no shortages areallowed). The following data are given:Pi number of units of product i that could be producedper year if the machine were entirely devoted toproducing product iDi annual demand for product iKi cost of setting up production for product ihi cost of holding one unit of product i in inventoryfor one yeara Suppose there are N cycles per year. Assuming thatduring each cycle, a fraction N1of all demand for eachproduct is met, determine the annual holding cost andthe annual setup cost.b Let qi* be the number of units of product i producedduring each cycle. Determine the optimal value of N(call it N*) and qi*. c Let EROQi be the optimal production run size forproduct i if…During the next four months, a customer requires,respectively, 500, 650, 1000, and 700 units of acommodity, and no backlogging is allowed (that is,the customer’s requirements must be met on time).Production costs are $50, $80, $40, and $70 per unitduring these months. The storage cost from one monthto the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the endof month 4 can be sold for $60. Assume there is nobeginning inventory.a. Determine how to minimize the net cost incurred inmeeting the demands for the next four months.b. Use SolverTable to see what happens to the decisionvariables and the total cost when the initial inventoryvaries from 0 to 1000 in 100-unit increments. Howmuch lower would the total cost be if the companystarted with 100 units in inventory, rather than none?Would this same cost decrease occur for every100-unit increase in initial inventory?Based on Zangwill (1992). Murray Manufacturingruns a day shift and a night shift. Regardless of thenumber of units produced, the only production costduring a shift is a setup cost. It costs $8000 to run theday shift and $4500 to run the night shift. Demand forthe next two days is as follows: day 1, 2000; night 1,3000; day 2, 2000; night 2, 3000. It costs $1 per unitto hold a unit in inventory for a shift.a. Determine a production schedule that minimizesthe sum of setup and inventory costs. All demandmust be met on time. (Note: Not all shifts have tobe run.)b. After listening to a seminar on the virtues of theJapanese theory of production, Murray has cut thesetup cost of its day shift to $1000 per shift and thesetup cost of its night shift to $3500 per shift. Nowdetermine a production schedule that minimizes thesum of setup and inventory costs. All demand mustbe met on time. Show that the decrease in setupcosts has actually raised the average inventorylevel. Is this reasonable?