Find the solutions: 1.0bjectives 2.Decision Variables 3. Certainty 4.. Parameters
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- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?Problem: A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50, and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and a tiller are rented. The tractor is available for 150 hours, and the tiller is available for 200 hours. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. How many acres of each crop should be planted to maximize the farmer’s profit? (Let W be the number of acres of wheat to be planted, B the number of acres of barley to be planted and P the profit) (a) What is the objective function for the problem? (b) Excluding the non-negative constraint, how many constraints does the problem have? (c) What is the linear programming model of the problem?Problem 3 Carrington Oil produces gas 1 and gas 2 from two types of crude oil: crude 1 and crude 2. Gas 1 is allowed to contain up to 4% impurities, and gas 2 is allowed to contain up to 3% impurities. Gas 1 sells for $72 per barrel, whereas gas 2 sells for $84 per barrel. Up to 4200 barrels of gas 1 and up to 4300 barrels of gas 2 can be sold. The cost per barrel of each crude, their availability, and the level of impurities in each crude are listed in the file. Before blending the crude oil into gas, any amount of each crude can be "purified" for a cost of $3.50 per barrel. Purification eliminates half of the impurities in the crude oil. Determine how to maximize profit. Use SolverTable to determine how an increase in the availability of crude 1 affects the optimal profit. Use SolverTable to determine how an increase in the availability of crude 2 affects the optimal profit. Use SolverTable to determine how a change in the price of gas 2 changes the optimal profit and the types of…
- PROBLEM 6 An investment firm has $1 million to invest in stocks, bonds, certificates of deposit, and real estate. The firm wishes to determine the mix of investments that will maximize the cash value at the end of 6 years. Opportunities to invest in stocks and bonds will be available at the beginning of each of the next 6 years. Each dollar invested in stocks will return $1.20 (a profit of $0.20) 2 years later; the return can be immediately reinvested in any alternative. Each dollar invested in bonds will return $1.40 3 years later; the return can be reinvested immediately. Opportunities to invest in certificates of deposit will be available only once, at the beginning of the second year. Each dollar invested in certificates will return $1.80 four years later. Opportunities to invest in real estate will be available at the beginning of the fifth and sixth years. Each dollar invested will return $1.10 one year later. To minimize risk, the firm has decided to diversify its…Problem 2 Sunblessed Juice Company sells bags of oranges and cartons of orange juice. Sunblessed grades oranges on a scale of 1 (poor) to 10 (excellent). At present, Sunblessed has 100,000 pounds of grade 9 oranges and 120,000 pounds of grade 6 oranges on hand. The average quality of oranges sold in bags must be at least 7, and the average quality of the oranges used to produce orange juice must be at least 8. Each pound of oranges that is used for juice yields a revenue of $1.50 and incurs a variable cost (consisting of labor costs, variable overhead costs, inventory costs, and so on) of $1.05. Each pound of oranges sold in bags yields a revenue of $1.50 and incurs a variable cost of $0.70. Determine how Sunblessed can maximize its profit. Use SolverTable to determine how a change in the cost per bag of oranges changes the optimal solution. Use SolverTable to determine how a change in the amount of grade 9 oranges available affects the optimal solution. Use SolverTable to determine…Problem 6. Rylon Corporation manufactures Brute cologne and Chanelle perfume. The raw material needed to manufacture each type of fragrance can be purchased for $60 per pound. Processing 1 pound of raw material requires 1 hour of laboratory time. Each pound of processed raw material yields 3 ounces of Regular Brute cologne and 4 ounces of Regular Chanelle perfume. Regular Brute can be sold for $140 per ounce and Regular Chanelle for $120 per ounce. Rylon also has the option of further processing Regular Brute and Regular Chanelle to produce Luxury Brute, sold at $360 per ounce, and Luxury Chanelle, sold at $280 per ounce. Each ounce of Regular Brute processed further requires an additional 3 hours of laboratory time and a $40 processing cost and yields 1 ounce of Luxury Brute. Each ounce of Regular Chanelle processed further requires an additional 2 hours of laboratory time and a $40 processing cost and yields 1 ounce of Luxury Chanelle. Each year, Rylon has 6000 hours of laboratory…
- Optimization Problem: Emesto is to plant a garden with two types of tree: palms and conifers. He is to plant at least 10, but not more than 80 palms. He is to plant at least 5, but not more than 40 conifers. He cannot plant more than 100 trees in total. Each palm needs 20 litres of water each day and each conifer needs 60 litres of water each day. There are 3000 litres of water available each day. Ernesto makes a profit of €2 on each palm and €1 on each conifer that he plants and he wishes to maximise his profit. Emesto plants x palms and y conifers.Problem 2: Comp-Max Computers assembles computers and computer equipment. It is about to start production of threenew types of computers, called model X, Y, and Z, respectively. Each type will require assembly time, inspection time, and storage space. The availability of each of these resources is limited. Specifically, available assembly time is 400 hours, available inspection time is 300 hours, and available storage space is 500 cubic feet (about 14.2 ms). The amount of each resource required for the different products is reported in the table below. Model X earns a profit of $100 per unit, model Yearns a profit of $125 per unit, and model 2 earns a profit of $200 per unit. Due to some prior agreements with customers, Comp-Max must produce at least 12 model X computers. In addition, management requires that the fraction of total production made up of model 2 computers must not exceed 25%. RESOURCE REQUIREMENTS Assembly time Inspection time Storage space MODEL hrs/unit hrsJunit cu.…Problem There are three factories on the Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $1000 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $2000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.30 ton. The state wants to reduce the amount of P 1in the river by at least 30 tons and the amount of P2 by at least 40 tons. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Use SolverTable to investigate the effects of increases in the minimal reductions required by the state. Specifically, see what…
- A chocolate maker has contracted to operate a small candy counter in a fashionable store. To startwith, the selection of offerings will be intentionally limited. The counter will offer a regular mixof candy made up of equal parts of cashews, raisins, caramels, and chocolates, and a deluxe mixthat is one-half cashews and one-half chocolates, which will be sold in one-pound boxes. In addition, the candy counter will offer individual one-pound boxes of cashews, raisins, caramels, andchocolates.A major attraction of the candy counter is that all candies are made fresh at the counter. However, storage space for supplies and ingredients is limited. Bins are available that can hold theamounts shown in the table.IngredientCapacity(pounds per day)Cashews 120Raisins 200Caramels 100Chocolates 160In order to present a good image and to encourage purchases, the counter will make at least 20boxes of each type of product each day. Any leftover boxes at the end of the day will be removedand given to a…The minimum-cost flow problem could be applied_________ Option- 1. by a telephone company attempting to lay out wires in a new housing development. 2. by a forest ranger seeking to minimize the risk of forest fires. 3. None of the choices. 4. by an airline laying out flight routes. 5. All of the choices are correct. Which of the following is not an assumption of a shortest path problem? 1. Associated with each link or arc is a nonnegative number called its length, 2. The objective is to find a shortest path from the origin to the destination. 3. The lines connecting certain pairs of nodes always allow travel in either direction. 4. None of the choices. 5. A path through the network must be chosen going from the origin to the destination.The government is auctioning off oil leases at twosites. At each site, 100,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickensare bidding for the oil. Government rules state that nobidder can receive more than 40% of the land beingauctioned. Cliff has bid $1000 per acre for site 1 landand $2000 per acre for site 2 land. Blake has bid $900per acre for site 1 land and $2200 per acre for site2 land. Alexis has bid $1100 per acre for site 1 landand $1900 per acre for site 2 land.a. Determine how to maximize the government’srevenue with a transportation model.b. Use SolverTable to see how changes in thegovernment’s rule on 40% of all land beingauctioned affect the optimal revenue. Why canthe optimal revenue not decrease if this percentage required increases? Why can the optimalrevenue not increase if this percentage requireddecreases?