Jim Jones manufactures inexpensive set-it-up-yourself furniture for students. He currently makes two products – bookcases and tables. Each bookcase contributes $24 to profit, and each table, $20. Each product passes through two manufacturing points, cutting and finishing. Bookcases take 4 hours a unit in cutting and 4 hours in finishing. Tables require 3 hours a unit in cutting and 5 in finishing. There are currently 40 hours available in cutting and 50 in finishing. Determine the optimum solution. Use graphic linear programming to find the product mix that produces the maximum profit for Jim.
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Jim Jones manufactures inexpensive set-it-up-yourself furniture for students. He currently makes two products – bookcases and tables. Each bookcase contributes $24 to profit, and each table, $20. Each product passes through two manufacturing points, cutting and finishing. Bookcases take 4 hours a unit in cutting and 4 hours in finishing. Tables require 3 hours a unit in cutting and 5 in finishing. There are currently 40 hours available in cutting and 50 in finishing. Determine the optimum solution. Use graphic linear programming to find the product mix that produces the maximum profit for Jim.
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- The MFA Co. Ltd. presently moves pallet loads of cans from production to the truck dock for loading. The loading dock foreman claims that due to increased production the company needs to purchase five new fork trucks and to hire five persons to operate these trucks. Using the present equipment (fork trucks) the maximum load of cans that can be transported is 1500 lb. at a 13.5” load center. The fork truck currently in use is manufacturer - rated for 3,000 lb. at the 24” load center. Question: Can the pallet load capacity be increased? What, if any, new equipment is required?Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. (ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit. Pickson Luthiers Corporation Data Guitar Model Selling price/Unit Variable cost/Unit Min Sales Max Sales ScarCT 750.00 660.00 0 2500 Dela Mort 788.00 680.00 0 2000 Warax 800.00 700.00 100 1000 Invazen 850.00 800.00 80 500 Production rates (units/hour) ScarCT Dela Mort Warax Invazen Hours Available Assembly - 35 25 20 220 Painting 35 20 15 10 220 Sound Testing 20 10 20 18 220 Inspection 10 12 8 5 220 Packaging 9 10 5 8 220 Use a linear optimization model based on the data to answer the following…A company produces two products: A and B. Prod-uct A sells for $11 per unit and product B sells for $23 per unit. Producing a unit of product A requires two hours on assembly line 1 and one unit of raw ma-terial. Producing a unit of product B requires two units of raw material, one unit of A, and two hours on as-sembly line 2. On line 1, 1300 hours of time are avail-able, and 500 hours are available on line 2. A unit of raw material can be bought (for $5 a unit) or produced(at no cost) by using two hours of time on line 1.a. Determine how to maximize profit.b. The company will stop buying raw material whenthe price of raw material exceeds what value? (UseSolverTable.)
- Knott’s Industries manufactures standard and superpremium backyard swing sets. Currently it has four identi-cal swing-set-making machines, which are operated 250days per year and 8 hours each day. A capacity cushionof 20 percent is desired. The following information is alsoknown:Standard ModelSuper PremiumModelAnnual Demand 20,000 10,000Standard Processing Time 7 min 20 minAverage Lot Size 50 30Standard Setup Time per Lot 30 min 45 mina. Does Knott’s have sufficient capacity to meet annualdemand?b. If Knott’s was able to reduce the setup time for the SuperPremium Model from 45 minutes to 30 minutes, wouldthere be enough current capacity to produce 20,000 unitsof each type of swing set?Western Chassis produces high-quality polished steel and aluminum sheeting and two lines ofindustrial chassis for the rack mounting of Internet routers, modems, and other telecommunicationsequipment. The contribution margin (contribution toward profit) for steel sheeting is $0.40 per poundand for aluminum sheeting is $0.60 per pound. Western earns $12 contribution on the sale of aStandard chassis rack and $15 contribution on a Deluxe chassis rack. During the next productioncycle, Western can buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or inchassis. Similarly, 20,400 pounds of aluminum are available. One standard chassis rack requires 16pounds of steel and 8 pounds of aluminum. A Deluxe chassis rack requires 12 pounds of each metal.The output of metal sheeting is restricted only by the capacity of the polisher. For the next productioncycle, the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting. Chassismanufacture can be…Dana’s Ribbon World makes award rosettes. Following is information about the company: Variable cost per rosette $ 2.00 Sales price per rosette $ 6.00 Total fixed costs per month $ 6000.00 Required: 1. Suppose Dana’s would like to generate a profit of $1,120. Determine how many rosettes it must sell to achieve this target profit. 2. If Dana’s sells 2,140 rosettes, compute its margin of safety in units, in sales dollars, and as a percentage of sales. 3. Calculate Dana’s degree of operating leverage if it sells 2,140 rosettes. 4a. Using the degree of operating leverage, calculate the change in Dana’s profit if unit sales drop to 1,819 units. 4b. Prepare a new contribution margin income statement to verify change in dana's profit.
- Quitmeyer Elec-tronics Incorporated manufactures the following six microcomputer peripheral devices: internal mo-dems, external modems, graphics circuit boards, CD drives, hard disk drives, and memory expansionboards. Each of these technical products requirestime, in minutes, on three types of electronic testingdevices, as shown in the table on this page.The first two test devices are available 120hours per week. The third (device 3) requires morepreventive maintenance and may be used only 100 hours each week. The market for all six computer components is vast, and Quitmeyer Electronics be-lieves that it can sell as many units of each product as it can manufacture. The table that follows summa-rizes the revenue and material cost for each product: DEVICE REVENUE PERUNIT SOLD ($) MATERIAL COSTPER UNIT ($)Internal modem 200 35External modem 120 25Graphics circuit board 180 40CD drive 130 45Hard disk drive 430 170Memory expansionboard 260 60 In addition, variable labor costs are $15…Rene steering makes 100 000 steering wheels per month. The firm works for 20 days in month, each day comprises of three 8 hour shifts. An assembly worker produces 10 steering wheels per hour; the firm needs ----- number of workers for each shift?PRODUCT MIX: The JP Manufacturing Company produces two products. Resource requirements for production are given in the table. There are 1500 hours of assembly worker hours available per week, 600 hours of paint time, and 200 hours of the inspection time. Regular customers will demand at least 150 units of the regular line and 90 of the super. Formulate an LP model that will determine the optimal product mix on a weekly basis. Product Profit contribution Assembly time (hr) Paint time (hr) Inspection time (hr) Product A 50 1 1/2 1/5 Product B 75 1.5 3/4 1/5
- Kala is one of the top manufacturer of ukuleles. The manufacturer produces three different types of ukuleles. Its Concert produce $6 in profit per unit; its Soprano produce $4 in profit per unit; and its Tenor produce $8 in profit per unit. Each type of ukulele passes through three manufacturing stages as a part of the entire production process. The three process centers of modelling, curing and assembly has an available production time per day of 12 hours, 14 hours and 16 hours, respectively. To produce one hundred units of Concert, the time required for the process of modelling, curing and assembly is 2 hours, 3 hours and 2 hours, respectively. To produce one hundred units of Soprano, 2 hours of modelling, 2 hours of curing and 1 hour of assembly is required. Whereas 4 hours of modelling, 2 hours of curing and 2 hours of assembly is required to produce one hundred units of Tenor. Sensitivity report of the problem is given as below where C = unit of Concert to be produced each day, S=…An assembly line requires two components: gadjits and widjits. Gadjits are produced by center 1 and widjits are produced by center 2. Each unit of the end item, called a jit-together, requires 3 gadjits and 2 widjits. The daily production quota on the assembly line is 750 jit-togethers. The container for gadjits holds 70 units. The policy variable for center 1 is set at 0.03. The average waiting time for container of gadjits is 0.08 day, and 0.05 day is needed to produce a container. The container for widjits holds 60 units, and the policy variable for center 2 is 0.09. The average waiting time per container of widjits is 0.16 day, and the time required to process a container is 0.26 day. a. How many containers are needed for gadjits? containers. (Enter your response rounded up to the next whole number.)An assembly line requires two components: gadjits and widjits. Gadjits are produced by center 1 and widjits are produced by center 2. Each unit of the end item, called a jit-together, requires 3 gadjits and 2 widjits. The daily production quota on the assembly line is 750 jit-togethers. The container for gadjits holds 70 units. The policy variable for center 1 is set at 0.03. The average waiting time for a container of gadjits is 0.08 day, and 0.05 day is needed to produce a container. The container for widjits holds 60 units, and the policy variable for center 2 is 0.09. The average waiting time per container of widjits is 0.16 day, and the time required to process a container is 0.26 day. a. How many containers are needed for gadjits? 5 containers. (Enter your response rounded up to the next whole number.) b. How many containers are needed for widjits? containers. (Enter your response rounded up to the next whole number.)