Having suffered an embarrassing defeat in Hobshire, Achlúk is rearming his army of orcs with axes, maces, and spears. This time, his budget is tight, and he wants to spend as little as possible but still inflict at least 8,000 units of damage on medium targets and 4,800 units of critical damage while keeping the total weight to no more than 5,000 pounds. What should his weapons arsenal look like, and how much will it cost? Weapon Cost (gold pieces) Damage to Medium Targets Critical Damage Weight (pounds) Axe (Throwing) 8 12 Javelin 1 6 12 2 Longsword 15 8. 32 4 Mace (Light) 5. 6. 12 4 Spear 24 Axes Maces Spears How much will it cost? gold pieces
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- Markus, Inc., has harvested 400 tons of lumber from a pine forest located outside of Manchester, 200 tons from a forest near Seattle, and 150 tons from a forest outside of Portland. Japan has placed an order for 300 tons at a price of $1200 per ton, Taiwan needs 300 tons and will pay $1000 per ton, and Singapore wants 250 tons at $1000 per ton. It costs Markus, Inc. $500 to get each ton from the pine forest to the port in Manchester, $400 per ton to the port in Seattle, and $300 per ton to Portland. Assume that each pine forest only supplies its closest port. The following table provides the cost for shipping each ton by sea from these ports to the respective countries: ________________________________________________________________________ SHIPPING COST ($/TON) OF LUMBER BY SEA TO: FROM JAPAN TAIWAN SINGAPORE Manchester 250 250 200 Seattle 250 200 200 Portland…Erica is going to fly to London on August 5th and return home on August 20th. It is now July 1st. On July 1st, she may buy a one-way ticket (for $350) or a round-trip ticket (for $660). She may also wait until August 1st when a one-way ticket will cost $370 and a round-trip ticket $730. It is possible that between July 1st and August 1st, her sister (who works for the airline) will be able to obtain a free one-way ticket for Erica. The probability that her sister will obtain the free ticket is 0.3. If Erica has bought a round trip ticket on July 1st and her sister has obtained the free ticket, she may return “half” of her round-trip to the airline. In this case her total cost will be $330 plus a penalty of $50. Use a decision tree to determine Erica’s lowest expected cost of obtaining a round-trip ticket to London.The Big Bang Novelty Company (BBNC) makes 3 types of noise?makers: Toot, Wheet, and Honk. A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 20 minutes, has two feathers, and is sprinkled with 0.5 ounces of sequin powder. The Honk requires 30 minutes, three feathers, and 1 ounce of sequin powder. The unit profits are $0.45 per Toot, $0.55 per Wheet, and $0.70 per Honk. The following resources are available: 80 hours of labor, 360 feathers, and 90 ounces of sequin powder. BBNC would like to maximize the overall profit from the noise-makers. (a) Write the linear programming model. Express labor time in minutes in LP formulationb) Solve using Excel Solver. How much of the resources (labor, feathers, and sequin powder) will be used by the optimal solution? If the availability of labor increases by 10 hours, what is the optimal total profit? If the unit profit of Wheet is actually only $0.30 instead of $0.55, will this change the solution? How many of each…
- Markus, Inc., has harvested 400 tons of lumber from a pine forest located outside of Manchester, 200 tons from a forest near Seattle, and 150 tons from a forest outside of Portland. Japan has placed an order for 300 tons at a price of $1200 per ton, Taiwan needs 300 tons and will pay $1000 per ton, and Singapore wants 250 tons at $1000 per ton. It costs Pine Trees, Inc. $500 to get each ton from the pine forest to the port in Manchester, $400 per ton to the port in Seattle, and $300 per ton to Portland. Assume that each pine forest only supplies its closest port. The following table provides the cost for shipping each ton by sea from these ports to the respective countries: ________________________________________________________________________ SHIPPING COST ($/TON) OF LUMBER BY SEA TO: FROM JAPAN TAIWAN SINGAPORE Manchester 250 250 200 Seattle 250 200 200 Portland…A goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.Bilbo Baggins wants to save money to meet threeobjectives. First, he would like to be able to retire 30 years from now with a retirementincome of $23,000 per month for 20 years, with the first payment received 30 yearsand 1 month from now. Second, he would like to purchase a cabin in Rivendell in10 years at an estimated cost of $320,000. Third, after he passes on at the end of the20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to hisnephew Frodo. He can afford to save $2,100 per month for the next 10 years. If hecan earn an 11 percent EAR before he retires and an 8 percent EAR after he retires,how much will he have to save each month in Years 11 through 30?
- Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $400 and $800, respectively. Assume initially that Patz can sell all that is produced of either component. Part A requires two hours of assembly, and B requires five hours of assembly. The firm has 400 assembly hours per week. What if market conditions are such that Patz can sell at most 100 units of Part A and 80 units of Part B? Express the objective function with its associated constraints for this case. Objective function: Max Z = $400 A + $800 B Assembly-hour constraint fill in the blank 7 A + fill in the blank 8 B ≤ fill in the blank 9 Demand constraint for Part A A ≤ fill in the blank 10 Demand constraint for Part B B ≤ fill in the blank 11 Identify the optimal mix and its associated total contribution margin.Component A $fill in the blank 12 units Component B $fill in the blank 13 units Total contribution $fill in the blank 14Suppose a certain 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 rods is $2,200, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,300. Manufacturing costs are $12 for each 4-cylinder connecting rod and $16 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. Let x4 = 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…3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds
- Vivian and Wayne are planning on going to Lamazenatural childbirth classes. Lamaze classes meet once a weekfor five weeks. Each class gives 20% of the knowledge neededfor “natural” childbirth. If Vivian and Wayne finish theirclasses before the birth of their child, they will forget duringeach week 5% of what they have learned in class. To maximizetheir expected knowledge at the time of childbirth, duringwhich week of pregnancy should they begin classes? Assumethat the number of weeks from conception to childbirthfollows the probability distribution given in Table 9. Week of Birth Probability36 .0537 .1539 .2040 .3041 .1542 .1043 .05A company wishes to plan its production of two items with seasonal demands over a 12-month period. The monthly demand of item1 is 100 units during the months of October, November and December; 10 units during the months of January, February, March and April; and 30 units during the remaining months. The demand of item2 is 50 units during the months of September through December and 15 units during the remaining months. Suppose that the unit product cost of item1 and item2 is 5000 TL and 8000 TL, respectively, if they are manufactured before June. After June, the unit costs are reduced to 4500 TL and 7000 TL because of the installation of an improved manufacturing system. Item1 requires 1 unit of a key component and item2 requires 2 units. The availability of this key component is 120 units per month during January- September and 150 units per month during October-December. Furthermore, each unit of item1 occupies 2 m3 and each item2 occupies 4 m3 of inventory. Suppose that the maximum…Steve's Scooer plans to sell it standard scooter for $500 and it chrome for $650. Steve purchases the standard scooter for $150 and Chrome for $250. Steve expects to sell one standard scooter for every three chrome scooter. Steve's monthly fixed cost are $263000. How many of each scooter must Steve sell each month to break even? and how many of each scooter must Steve sell each month to earn $697000?