Target Section 2 Skill WS - Linear Programming

Transcription

1 Intermediate Algebra V Ab0epK GKVuPt`aU wsiorfdtqwhaprgel MLnLECl.B U EArlWll cruiyglhdtwsk trnecsxexrovpendh. Target. - Section Skill WS - Linear Programming Name The variables have been defined, the objective and constraints have been written. Now, you must finish each of the linear programming problems below. Start by graphing the constraints, shading, and testing vertices. ) You need to buy some filing cabinets. You know that Cabinet X costs $ per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $0 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $0 for this purchase, though you don't have to spend that much. The office has room for no more than 7 square feet of cabinets. How many of which model should you buy, in order to maximize storage volume? X is the number of Cabinet X Y is the number of Cabinet Y V = X + Y X + 0Y 0 X + Y 7 Teacher y x E LR0_gi nksudt]at ms[obfmttw\a]rleu QL`LTCG.v f davlglc criicgzhetws] trqezs\ehrxvmeode.s z nmtadd]ep gwaixtqhc WI[nEfOiJnqixtSe^ iaml\gzenbornaw OV. --

2 ) A snack bar cooks and sells hamburgers and hot dogs during football games. To stay in business, it must sell at least hamburgers but can not cook more than 0. It must also sell at least 0 hot dogs, but can not cook more than 70. The snack bar can not cook more than 90 items total. The profit on a hamburger is cents, and the profit on a hot dog is cents. How many of each item should it sell to make the maximum profit? H is the number of hamburgers D is the number of hot dogs P = 0.H + 0.D H ³, H 0 D ³ 0, D 70 H + D s GS0rVO IK_uptxaJ qspo]f[thwzaprcex tlhlbct.w z yaplzl_ pr^imgrhptisf CrlepsceZrBvTeNdU.c u cmjatddeb cwhiqtdh_ ei]npfridnuiitkem RAnlLgFeBblrbak EO. --

3 ) In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of grams (g) of fat, g of carbohydrates, and g of protein. But the rabbits should be fed no more than five ounces of food a day. Rather than order rabbit food that is custom blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains g of fat, g of carbohydrates, and g of protein per ounce, and costs $0.0 per ounce. Food Y contains g of fat, g of carbohydrates, and g of protein per ounce, at a cost of $0.0 per ounce. What is the optimal blend of Food X and Food Y? X is the number of ounces of Food X Y is the number of ounces of Food Y C = 0.X + 0.Y X + Y ³ X + Y ³ X + Y ³ X + Y F MB0RWc BKduYtgab WSKomfttHwSaIrLem HLGLaCy.^ U fafllle lrmimgzhctysi Hrpe^sneyrSvSexde.d [ tmqatdheq pwqimt^hg OIxn\ffinnkiHtveB QARlEgHetbKroai yt. --

4 ) You are about to take a test that contains questions of type A worth points and type B worth 7 points. You must answer at least of type A and of type B, but time restricts answering more than of either type. In total, you can answer no more than. How many of each type of question must you answer, assuming all of your answers are correct, to maximize your score? What is your maximum score? A is the number of type A questions B is the number of type B questions S = A + 7B A ³, A B ³, B A + B M xl0[re wkzuqtgae dsjojfltdwtatrhek SLhLoCp.w w UADlClH brfirgphztlsw BrLeysbeNrNvReedt.O A tmgawdeef NwTiNtzhi `IlnyfEimn\iZtoeE _AVlmgjecbEr[aR mq. --

5 ) Marcus is creating a low-fat pie crust recipe for his pie shop. Butter has six grams of saturated fat and one gram of unsaturated fat per tablespoon. Vegetable shortening has one gram of saturated fat and four grams of unsaturated fat per tablespoon. In the recipe, the butter and vegetable shortening will not be more than tablespoons. The butter and vegetable shortening combine for at least grams of saturated fat and at least grams of polyunsaturated fat. Minimize the number of calories in the recipe if butter has 0 calories per tablespoon and vegetable shortening has calories per tablespoon. B is the number of tablespoons of Butter V is the number of tablespoons of Vegetable Shortening C = 0B + V B + V B + V ³ B + V ³ y Bh0e^M `KouXttax IShoFf_tGwOajrGev FLKLRCg.P H TAUlolw Qr`iJgAhytsse BrCersHeurovTegdk.\ P ^MKaDdxed WwgiBtZhh nizn_fvivndiutoeg FAIlZgBeLb]rYaB CL. --

6 Answers to Target. - Section Skill WS - Linear Programming ) (, ) is the solution, which means Cabinet X's and Cabinet Y's for a maximum volume of 0 f t y 7 9 x ) (0, 0) is the solution, which means that 0 hamburgers and 0 hot dogs should be sold to make the maximum profit of $ ) (, 0) is the solution, which means ounces of Food X and 0 ounces of Food Y for a minimum cost of $.0. K l_0p[m XKvuRtwaZ ^SLoqf`tVwxahrRel JLlLdCZ.f X ^AklvlK grzimgkhnttss CrweKs^e^rRvjewdq.N -- s tm\ahdzew xw\iatmhs kion`fxitnlidtjec VAElMgAePblr`aJ bl.

7 ) (, ) is the solution, which means you should choose to answer questions of type A and questions of type B for a maximum score of points. 0 0 ) (, ) is the solution, which means that tablespoons of Butter and tablespoons of Vegetable Shortening should be used for a minimum of 0 calories ` EL0XJt tkgukt_al yskohfbtswcabrxem ILvLWCd.v u iailklv krdidgvhftzsx crdepsse\rfv_erdl.y A BMVapdreG BwziStOhe gign]fhiwnhiytuef taulgglegberdaz hx. -7-