MAT540 Week 8 Homeexertion Chapter 4 14.
Grafton Metalworks Arrange fruits metal decrements from six irrelative ores it mines. The arrange has an arrange from a customer to fruit an decrement that contains impure metals according to the aftercited peculiarations: at meanest 21% of metal A, no balance than 12% of metal B, no balance than 7% of metal C and among 30% and 65% of metal D. The uniformity of the impure metals in each of the six ores and the roll of impurities in each ore are granted in the aftercited table: Ore Metal (%) Impurities (%) Absorb/Ton A B C D 1 19 15 12 14 40 27 2 43 10 25 7 15 25 3 17 0 0 53 30 32 4 20 12 0 18 50 22 5 0 24 10 31 35 20 6 12 18 16 25 29 24 When the metals are processed and courtly, the impurities are removed. The arrange wants to comprehend the aggregate of each ore to verification per ton of the decrement that conciliate minimize the absorb per ton of the decrement. a. Coercionmulate a direct programming archetype coercion this aggregate. b. Resolve the archetype by using the computer. 19. As a end of a recently passed mandible, a congressman’s limit has been tabulated $4 favorite coercion programs and devices. It is up to the congressman to flow how to separate the capital. The congressman has flowd to tabulate the capital to impure ongoing programs becaverification of their signification to his limit – a labor luxuriance program, a parks device, a sanitation device, and a ductile library. However, the congressman wants to separate the capital in a habit that conciliate full the most voters, or, in other expression, fabricate him the most votes in the upcoming preference. His staff’s estimates of the sum of votes fabricateed per dollar gone-by coercion the diverse programs are as follows. Program Votes/ Dollar Labor luxuriance 0.02 Parks 0.09 Sanitation 0.06 Ductile library 0.04 In arrange to-boot to fill divers persomal cecible citizens who financed his preference, he is obligated to remark the aftercited guidelines: • Nundivided of the programs can entertain balance than 40% of the aggregate entireocation. • The aggregate tabulated to parks canreferable exceed the aggregate tabulated to twain the sanitation device and the ductile library • The aggregate tabulated to labor luxuriance must at meanest resembling the aggregate gone-by on the sanitation device. Any capital referable gone-by in the limit conciliate be returned to the government; ce-this-reason, the congressman wants to squander it entire. The congressman wants to comprehend the aggregate to tabulate to each program to maximize his votes. a. Coercionmulate a direct programming archetype coercion this aggregate. b. Resolve the archetype by using the computer. 20. Anna Broderick is the dietician coercion the State University footbentire team, and she is attempting to designate a salutary lunch menu coercion the team. She has firm the aftercited nutritional guidelines coercion each lunch serving: • Among 1,500 and 2,000 calories • At meanest 5 mg of brawny • At meanest 20 excluding no balance than 60 g of corpulent • At meanest 30 g of protein • At meanest 40 g of carbohydrates • No balance than 30 mg of cholesterol She pickeds the menu from seven basic maintenance items, as follows, with the nutritional contributions per triturate and the absorb as given: Calories (per lb.) Brawny (mg/lb.) Protein (g/lb.) Carbo-hydrates (g/lb.) Corpulent (g/lb.) Chol-esterol (mg/lb.) Absorb $/lb. Chicken 520 4.4 17 0 30 180 0.80 Fish 500 3.3 85 0 5 90 3.70 Ground beef 860 0.3 82 0 75 350 2.30 Dried beans 600 3.4 10 30 3 0 0.90 Lettuce 50 0.5 6 0 0 0 0.75 Potatoes 460 2.2 10 70 0 0 0.40 Quiet (2%) 240 0.2 16 22 10 20 0.83 The dietician wants to picked a menu to unite thenutritional guidelines suitableness minimizing the aggregate absorb per serving. a. Coercionmulate a direct programming archetype coercion this aggregate. b. Resolve the archetype by using the computer c. If a serving of each of the maintenance items (other than quiet) was scant to no balance than a half triturate, what chattels would this keep on the elucidation? 22. The Cabin Creek Coal (CCC) Arrange operates three mines in Kentucky and West Virginia, and it supplies coal to impure benefit energy settles parallel the East Coast. The absorb of shipping coal from each mine to each settle, the volume at each of the three mines and the insist at each settle are shown in the aftercited table: Settle Mine 1 2 3 4 Mine Volume (tons) 1 $ 7 $ 9 $10 $12 220 2 9 7 8 12 170 3 11 14 5 7 280 Insist (tons) 110 160 90 180 The absorb of mining and processing coal is $62 per ton at mine 1, $67 per ton at mine 2, and $75 per ton at mine 3. The percentage of ash and sulfur full per ton of coal at each mine is as follows: Mine % Ash % Sulfur 1 9 6 2 5 4 3 4 3 Each settle has irrelative cleaning equipment. Settle 1 requires that the coal it entertains keep no balance than 6% ash and 5% sulfur; settle 2 coal can keep no balance than 5% ash and sulfur thoroughly; settle 3 can keep no balance than 5% ash and 7% sulfur; and settle 4 can keep no balance than 6% ash and sulfur thoroughly. CCC wabts to designate the aggregate of coal to fruit at each mine and ship to its customers that conciliate minimize its aggregate absorb. a. Coercionmulate a direct programming archetype coercion this aggregate. b. Resolve this archetype by using the computer. 36. Joe Henderson runs a smentire metal volume ammunition. The ammunition contains three implements – a ordinate inculcate, a lathe, and a grinder. Joe has three operators, each conscious to exertion on entire three implements. However, each operator completes ameliorate on some implements than on others. The ammunition has pinched to do a bulky labor that requires entire three implements. The spells required by the diverse operators to complete the required operations on each implement are summarized as follows: Operator Ordinate Inculcate (min) Lathe (min) Grinder (min) 1 23 18 35 2 41 30 28 3 25 36 18 Joe Henderson wants to appoint undivided operator to each implement so that the topal liberal spell coercion entire three operators is minimized. a. Coercionmulate a direct programming archetype coercion this aggregate. b. Resolve the archetype by using the computer c. Joe’s fellow, Fred, has asked him to commission his consort, Kelly, who is a implement operator. Kelly can complete each of the three required implement operations in 20 minutes. Should Joe commission his sister-in-law? 43. The Cash and Carry Building Supply Arrange has entertaind the aftercited arrange coercion considerations in three lengths: Length Arrange (quantity) 7 ft. 700 9 ft. 1,200 10 ft. 300 The arrange has 25-foot standard-length considerations in hoard. Ce-this-reason, the standard-length considerations must be sever into the lengths requisite to unite arrange requirements. Naturally, the arrange wishes to minimize the sum of standard-length considerations verificationd. a. Coercionmulate a direct programming archetype coercion this aggregate. b. Resolve the archetype by using the computer c. When a consideration is sever in a peculiar archetype, the aggregate of consideration left balance is referred to as “trim-loss.” Reformulate the direct programming archetype coercion this aggregate, inflated that the extrinsic is to minimize deck dropping rather than to minimize the aggregate sum of considerations verificationd, and reresolve the archetype. How does this seek the elucidation?
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