BE Prints, Inc. produces two types of offset printers: Chamber and Flicker. Demand for both products is booming and exceeds the company's ability to satisfy it. Most raw materials are plentiful, but production is limited by three factors: a shortage of steel rollers, gear cutting capacity and roller polishing capacity. Each Chamber offset printer requires 12 rollers, and each Flicker requires 10 rollers. Chamber requires 36 hours of gear cutting and 12 hours of polishing time, while Flicker requires 32 hours of gear cutting and 14 hours of polishing time. The company is able to buy 200 rollers per week, and it has 180 hours of gear cutting time and 150 hours of polishing time available per week. At current prices, the company will earn a profit of P30,000 on each Chamber printer made and P26,000 on each Flicker printer made. Formulate and solve the problem as a linear program to maximize its profit.
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- Carlo and Anita make mailboxes and toys in their craft shop near Lincoln. Each mailbox requires 1 hour of work from Carlo and 1 hourfrom Anita. Each toy requires 1 hour of work from Carlo and 4 hoursfrom Anita. Carlo cannot work more than 6 hours per week and Anita cannot work more than 12 hours per week. If each mailbox sells for $12 and each toy sells for $23, then how many of each should they make to maximize their revenue? What is their maximum revenue? Carlo and Anita should make, x mailboxes and y toys. Their maximum revenue is: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.The poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities. A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron. Formulate the linear programming model for this situation. Group of answer choices Min Z = $450C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Min Z = $400C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Max Z = $400C + $500A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Max Z = $400C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Min Z = $400C + $200A Subject to: 150C + 250A ≥ 400…
- Happy Dog Inc. produces three types of dog food. Puppy Blend is produced for dogs that are less than a year old, Adult Blend for dogs between 1 and 8 years old, and Geriatric Blend for dogs older than 8 years. Each blend, sold in 5 pound bags, has a unique recipe that requires, among other ingredients, exact quantities of certain raw materials. Chicken Fish Meal Soy Flour Demand (in5 lb. bags) Puppy Blend Adult Blend Geriatric Blend Availability of rawmaterial 2.5 lbs. 1.5 lbs. 1.0 lbs. 10,000 lbs. 1.0 lbs. 2.0 lbs. 2.0 lbs. 20,000 lbs. 0.5 lbs. 0.5 lbs. 1.0 lbs. 5,000 lbs. 2000 8000 1000 a. Formulate a linear programming model that produces as many bags of dog food as possible without exceeding the demand or the available supply of raw material.b. Reformulate the linear programming model if the company is now interested in maximizing their profit 1price - raw material cost2 from dog food production. Assume that Puppy Blend sells for $9.50 per bag, Adult Blend…(Need both parts a and b) During the next four months, a customer requires, respectively, 500, 650, 1000, and 700 units of a commodity, 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 unit during these months. The storage cost from one month to the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 can be sold for $60. Assume there is no beginning inventory. A. What is the objective function in this problem? B. What are the constraints in this problem? Write algebraic expressions for eachHot Breads, a popular baker in Dhaka makes two types of cakes. To make one dozen ofpremium pound cake requires 3 kilos of flour, 1 kilo sugar, and 1 kilo butter. Making one dozenof our best requires 6 kilos of flour, 0.5 kilo of sugar, and 1 kilo of butter. Hot bread has in itsstock 150 kilograms of flour, 22 kilograms of sugar, and 27.5 kilograms of butter. The premiumcakes sell for 20 taka per dozen and our best sells for 30 taka per dozen. How many dozens ofeach cake Hot Breads should make to maximize revenue?a. Write the information given in the question in a tabular format.b. Write the problem in a linear programming format.c. Indentify the feasible zone.d. Find the revenue maximizing levels of production for scrapers and brushes.e. Is there any excess capacity in any machine?f. Find the amount of excess capacity.
- Kevin runs a factory that makes stereo tuners. Each S100 takes 9 ounces of plastic and 6 ounces of metal. Each G150 requires 3 ounces of plastic and 9 ounces of metal. The factory has 360 ounces of plastic, 702 ounces of metal available, with a maximum of 24 S100 that can be built each week. If each S100 generates $13 in profit, and each G150 generates $8, how many of each of the stereo tuners should Kevin have the factory make each week to make the most profit? S100= G150= Best profit=A company must meet (on time) the following demands:quarter 1—30 units; quarter 2—20 units; quarter 3—40units. Each quarter, up to 27 units can be produced withregular-time labor, at a cost of $40 per unit. During eachquarter, an unlimited number of units can be produced withovertime labor, at a cost of $60 per unit. Of all unitsproduced, 20% are unsuitable and cannot be used to meetdemand. Also, at the end of each quarter, 10% of all unitson hand spoil and cannot be used to meet any futuredemands. After each quarter’s demand is satisfied andspoilage is accounted for, a cost of $15 per unit is assessedagainst the quarter’s ending inventory. Formulate an LP thatcan be used to minimize the total cost of meeting the nextthree quarters’ demands. Assume that 20 usable units areavailable at the beginning of quarter 1.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…
- VITRAN Bus Services purchases diesel fuel from Domino Gas Supply. In addition to fuel cost, Domino Gas Supply charges VITRAN Bus Services $250 per order to cover the expenses of delivering and transferring the fuel to VITRAN Bus Services storage tanks. The lead time for new shipment from Domino Gas Supply is 10 days, the cost of holding a gallon of fuel in the storage tanks is $0.04 per month, or $0.48 per year and the annual usage of fuel is 150,000 gallons. VITRAN Bus Services buses operate 300 days a year. What is the optimal order quantity for VITRAN Bus Services? How frequently should VITRAN Bus Services order to replenish the gasoline supply?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?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