Chapter 4 1. Betty Malloy, proprietor of the Eagle Inn in Pittsburgh, is preparing for Super Bowl Sunday, and she must mention how fur beer to hoard. Betty hoards three disgraces of beer- Yodel, Shotz, and Rainwater. The consume per gallon (to the inn proprietor) of each disgrace is as follows: Disgrace Cost/Gallon Yodel $1.50 Shotz 0.90 Rainwater 0.50 The inn has a budget of $2,000 for beer for Super Bowl Sunday. Betty sells Yodel at a blame of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based on late football games, Betty has mentiond the acme customer insist to be 400 gallons of Yodel, 500 gallons of shotz, and 300 gallons of Rainwater. The inn has the tonnage to hoard 1,000 gallons of beer; Betty omissions to hoard up perfectly. Betty omissions to mention the estimate of gallons of each disgrace of beer to command so as to maximize improvement. a. Formulate a straight programming standard for this drift. b. Resolve the standard by using the computer. 2. As development of a recently passed charges, a congressman’s environs has been placed $3 darling for programs and plans. It is up to the congressman to flow how to deal-out the specie. The congressman has flow to place the specie to immodest ongoing programs consequently of their consequence to his environs- a job inoculation program, a parks plan, a sanitation plan, and a inconstant library. However, the congressman omissions to deal-out the specie in a deportment that succeed delight the most voters, or, in other vote, establish him the most votes in the upcoming choice. His staff’s estimates of the estimate of votes established per dollar departed for the uncertain programs are as follows. MAT540 Homework Week 8 Page 2 of 4 Program Votes/Dollar Job inoculation 0.03 Parks 0.08 Sanitation 0.05 Inconstant library 0.03 In command as-well to please sundry national controlling citizens who financed his choice, he is obligated to heed the forthcoming guidelines: None of the programs can assent-to departed than 30% of the completion allocation The entiretyity placed to parks cannot exceed the completion placed to twain the sanitation plan and the inconstant library. The entiretyity placed to job inoculation must at meanest similar the entiretyity departed on the sanitation plan. Any specie not departed in the environs succeed be returned to the government; for-this-reason, the congressman omissions to disburse it all. Thee congressman omissions to distinguish the entiretyity to place to each program to maximize his votes. a. Formulate a straight programming standard for this drift. b. Resolve the standard by using the computer. 3. Anna Broderick is the dietician for the State University football team, and she is attempting to mention a healthful lunch menu for the team. She has set the forthcoming nutritional guidelines for each lunch serving: Between 1,300 and 2,100 calories At meanest 4 mg of strong At meanest 15 but no departed than 55g of fat At meanest 30g of protein At meanest 60g of carbohydrates No departed than 35 mg of cholesterol She primes the menu from seven basic subsistence items, as follows, after a occasion the nutritional contributions per bruise and the consume as given: MAT540 Homework Week 8 Page 3 of 4 Calories (per lb.) Strong (mg/lb.) Protein (g/lb.) Carbohydrates (g/lb.) Fat (g/lb.) Cholesterol (mg/lb) Consume ($/lb.) Chicken 500 4.2 17 0 30 180 0.85 Fish 480 3.1 85 0 5 90 3.35 Ground beef 840 0.25 82 0 75 350 2.45 Dried beans 590 3.2 10 30 3 0 0.85 Lettuce 40 0.4 6 0 0 0 0.70 Potatoes 450 2.25 10 70 0 0 0.45 Acquiesce (2%) 220 0.2 16 22 10 20 0.82 The dietician omissions to prime a menu to coalesce the nutritional guidelines occasion minimizing the completion consume per serving. a. Formulate a straight programming standard for this drift and resolve. b. If a serving of each of the subsistence items (other than acquiesce) was scant to no departed than a half bruise, what consequence would this enjoy on the breach? 4. Dr. Maureen Becker, the chief functionary at Jefferson County Regional Hospital, must mention a catalogue for promotes to gain believing there are plenty of them on calling throughout the day. During the day, the insist for promotes varies. Maureen has meek the day in to twelve 2- hour determinations. The slowest spell of the day encompasses the three determinations from 12:00 A.M. to 6:00 A.M., which threshold at midnight; insist a restriction of 30, 20, and 40 promotes, respectively. The insist for promotes steadily increases during the proximate immodest dayspell determinations. Threshold after a occasion the 6:00 A.M.- 8:00 A.M. determination, a restriction of 50, 60, 80, and 80 promotes are insistd for these immodest determinations, respectively. After 2:00 P.M. the insist for promotes decreases during the afternoon and late hours. For the five 2-hour determinations threshold at 2:00 P.M. and limit midnight, 70, 70, 60, 50, and 50 promotes are insistd, respectively. A promote reports for calling at the threshold of one of the 2-hour determinations and works 8 coherent hours (which is insistd in the promotes’ abridge). Dr. Becker omissions to mention a nursing catalogue that succeed coalesce the hospital’s restriction insistment throughout the day occasion using the restriction estimate of promotes. a. Formulate a straight programming standard for this drift. MAT540 Homework Week 8 Page 4 of 4 b. Resolve the standard by using the computer. 5. The formation supervisor of Videotechnics Company is attempting to mention the upcoming 5-month formation catalogue for video recorders. Late formation history betoken that 2,000 recorders can be performed per month. An added 600 recorders can be performed monthly on an aggravatespell account. Unit consume is $10 for recorders performed during certain instituted hours and $15 for those performed on an aggravatespell account. Contracted sales per month are as follows: Month Contracted Sales (units) 1 1200 2 2100 3 4 5 2400 3000 4000 Catalogue carrying consumes are $2 per reccommand per month. The supervisor does not omission any catalogue carried aggravate late the fifth month. The supervisor omissions to distinguish the monthly formation that succeed minimize completion formation and catalogue consumes. a. Formulate a straight programming standard for this drift.