3, 10, 11

chapter4I;l the initial simplex tableau. x2 2 s1 1g 2A0t 3. Find the solutions that can be read from the simplex tableau given below" x1x2x3sls2s3z 40121000 060800 0000219 -1 0 0 I 0 6 x1 x2 x3 sl s2 s3 Z- (Simplify your answer.) (Simplify your answer.) (Simplify your answer.) (Simplify your answer.) (Simplify your answer.) (Simplify your answer.) (Simplify your answer.) 2of6 chaptl} 6 10. State the dual problem for the following, but do not solve it" Minimize v7 = y1 + 3y, + 5y, + 8yo Subject to: 3yt+4yz+7yt+yq>-5 Yt + 3Yz + 3Yg + Ya> 10 Yr >0,Y2 >0,Y3 >0, Ya >0 Maximize z = Subject to: Xl+ x2 s1 <3 <6 <8 xr>0,x2>0 11. An animal food must provide 60 units of vitamins and 65 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 7 cents, a gram of meat byproducts 9 cents, and a gram of grain 10 cents. Complete parts (a) and (b) below. (a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost? First, set up the initial tableau for the dual maximum problem. Fill in the missing entries. x1x231S2S3Z -t 10l 0l 2.5 4.5 5 5100 3010 10 0 0 1 0 0 01 There is more than one optimal basic solution to this problem. The answer depends on whether the tie in the minimum ratio rule is broken by pivoting on the second row or third row of the dual. \A/hen pivoting on the second row of the dual, the mixture would contain grams of soybean meal, grams of meat byproducts, and grams of grain. When pivoting on the third row of the dual, the mixture would contain grams of soybean meal, grams of meat byproducts, and grams of grain. (Round to one decimalplace as needed.) (b) What is the minimum cost? The minimum cost is cents. 6 of6 (Round to one decimal place as needed.) C