MINIMIZING SNIPPING COSTS TMA manufactures 37-in. high-definition LCD televisions in two separate locations: Location I and Location II. The output at Location I is at most
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Find a shipping schedule that meets the requirements of both companies while keeping costs to a minimum.
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Chapter 3 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition
- If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.arrow_forwardSuppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.arrow_forward23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.arrow_forward
- TMA manufactures 37-in. high definition LCD televisions in two separate locations, Locations I and II. The output at Location I is at most 6000 televisions/month, whereas the output at Location II is at most 5000 televisions/month. TMA is the main supplier of televisions to the Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 4000 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping costs per television from the two TMA plants to the two Pulsar factories are as follows. To Pulsar Factories From TMA City A City B Location I $7 $3 Location II $8 $9 TMA will ship x televisions from Location I to city A and y televisions from Location I to city B. Find a shipping schedule that meets the requirements of both companies while keeping costs to a minimum. (x, y) $= Solve the linear programming problem by…arrow_forwardThe Lawson Fabric Mill Produces five different fabrics. Each fabric can be woven on one or more of the mill’s 36 looms. The sales department’s forecast of demand for the next month is shown in below Table 1, along with data on the selling price per yard, variable cost per yard, and purchase price per yard. The mill operates 24 hours a day and is scheduled for 30 days during the coming month. The mill has two types of looms: draw and regular. The draw looms are more versatile and can be used for all five fabrics. The regular looms can produce only three of the fabrics. The mill has a total of 36 looms: 8 are draw and 28 are regular. The rate of production for each fabric on each type of loom is given in below Table 2. The time required to change over from producing one fabric to another is negligible and does not have to be considered. The Lawson Fabric Mill satisfies all demand with either its own fabric or fabric purchased from another mill. Fabrics that cannot be woven at the…arrow_forwardThe Sentry Lock Corporation sells a variety of electronic goods through television shows. The company has a number of storages to keep the goods it sells, but also takes out a lease on additional storage space when required. During the next 5 months the company anticipates that it is going to need to take out a lease on the following amounts of additional storage space: Month 1 2 3 4 5 Square Feet(ft2) Needed 20,000 30,000 40,000 35,000 50,000 In the beginning of any month the company can take out a lease on additional space for one or more months at the following costs: Lease Term (months) 1 2 3 4 5 Cost per Sq. Ft. Leased $55 $85 $130 $165 $185 Therefore, for example, in the beginning of month 1 the company can take out a lease on as much space as it requires for four months at a cost of $165 per ft2 . Similarly, in the beginning of month 3 it can take out a lease on any amount of space for two months at a cost of $85 per ft2 . The company needs to determine the optimal way of…arrow_forward
- Tailwind, Inc., produces high-quality but expensive training shoes for runners. The Tailwind shoe, which sells for $210, contains both gas- and liquid-filled compartments to provide more stability and better protection against knee, foot, and back injuries. Manufacturing the shoes requires 10 separate tasks. There are 400 minutes available for manufacturing the shoes in the plant each day. Daily demand is 62. The information for the tasks is as follows: Fig. 1 Task A Performance Time (mins) 1 Predecessors 3 A 1 B B C, D A F Н G 1 4 E, H | 42326- BCDEFGHI - J a-b) The correct precedence relationship with one of the possible assignments of tasks using the "ranked positioned weight" to workstations is shown in c) The efficiency of the assembly line with 5 workstations shown in the figure chosen above= % (enter your response as a percentage rounded to one decimal place). d) The idle time for the assembly line per cycle = ☐ minute(s) (enter your response as a whole number). ☑ B E H → Fig. 2…arrow_forwardA company makes a single product on two separate production lines, A and B. Its labor force is equivalent to 1100 hoursper week, and it has $2800 outlay weekly on operating costs. It takes 1 hour and 5 hours to produce a single item on linesA and B, respectively. The cost of producing a single item is $8 on line A and $6 on line B. (Let the x refer to the number ofitems on line A and y refer to the number of items on line B.) (a) Write the inequality that expresses the labor information. (b) Write the inequality that expresses the cost information.arrow_forwardA company makes three components for sale. The components are processed on two machines: a shaper and a grinder. The time required. (in minutes) on each machine are as follows: Component Shaper Time Grinder Time A 6 4 B 4 5 C 4 2 The shaper is available for 7200 min. and grinder for 6600 min. No more than 200 units of component C can be sold, but up to 1000 units of each of the other components can be sold. In fact the company has orders for 600 units of component A that must be satisfied. The profit contributions for components A, B and C are $8, $6 and $9 respectively. Formulate the problem for deciding the production quantities. Solve the problem using Excel Solver. Run the sensitivity analysis report in Excel Solver. What are the objective coefficient ranges (Range of Optimality) for each coefficient. Interpret these. What are the dual prices for each constraint? Interpret these. What are the right-hand side ranges (Range of Feasibility)? Interpret them. If more time is…arrow_forward
- . Embassy motorcycles (EM) manufactures two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ-Rider engine require 6 hours of manufacturing time and each Lady-sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. Embassy’s motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can provide only up to 280 Lady sport frames for the next production period. Final assembly and testing requires 2 hours for each EZ-Rider model and 2.5 hours for each Lady-Sport model. A maximum of 1000 hours of assembly and…arrow_forwardThe amount of nitrogen (in lb/acre), phosphate (in lb/acre), and labor (in hr/acre) needed to grow honeydews, yellow onjons, and lettuce is given by the table to the right. Complete parts a and b. OA. Yes, the farmer should allot B. No, it is not possible to use all resources completely. acres for honeydew, for yellow onions, and acres for lettuce. Honeydews 120 Nitrogen Phosphate 180 Labor 5 a) If the farmer has 230 acres, 30,300 lb of nitrogen, 34,400 lb of phosphate, and 400 hours of labor, is it possible to use all resources completely? If so, how many acres should he allot for each crop? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ⒸA. Yes, the farmer should allot acres for honeydew, OB. No, it is not possible to use all resources completely. Yellow onions 150 acres for lettuce. 80 6 Lettuce b) Suppose everything is the same as in part a, except that 1180 hours of labor are available. Is it possible to use all resources…arrow_forwardDean Smith is dissatisfied with the time it takes to get a new faculty ID made and believes more servers will speed up service and reduce costs thanks to shorter lines. Prof. Karen is tasked to study the situation. Prof. Karen observes an average of 20 customers/hr arriving and each technician (service window) services 5 customers/hr, on average. Assume an M/M/s queue system. Prof. Karen calculates the operational cost of each server as $20/hr, and assumes a cost of waiting in the SYSTEM as $25/hr per customer. What is the optimal number of service windows to minimize total cost?arrow_forward
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