Use the simplex method to solve the following linear programming problem. Find y, 20 and Y220 such that 4y + y2 27, +44227, and w = 4y7 + 18y2 is minimizec The minimum is w= (Simplify your answers.) - aty - and y2=0 A company sells sets of Kitchen knives. A Basic Set consists of 2 utility knives and 1 chef's knife. A Regular Set consists of 2 utility knives, 1 chef's knife, and 1 slicer. A Deluxe Set consists of 3 utility knives, 1 chef's knife, and 1 slicer. The profit is $20 on a Basic Set, $60 on a Regular Set, and $80 on a Deluxe Set. The factory has on hand 1600 utility knives, 800 chef's knives, and 400 slicers. (a) If all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum profit? (b) A consultant for the company notes that more profit is made on a Regular Set than on a Basic Set, yet the result from part (a) recommends making up more Basic Sets than Regular Sets. She is puzzled how this can be the best solution How would you respond? (a) Find the objective function to be used to maximize profit. Letx, be the number of Basic Sets, let xz be the number of Regular Sets, and let xz be the number of Deluxe Sets. What is the objective function? z-OxOx+3x (Do not include the $ symbol in your answers.) (a) To maximize profit, the company should make up Basic Sets. Regular Sets, and Deluxe Sets (Simplify your answers.) The maximum profit is $ (Simplify your answer.) (b) Choose the correct answer below. O A. The Basic Set requires fewer knives. So, more Basic Sets can be made up than Regular Sets. This results in higher overall profit. OB. The Basic Set requires fewer knives. So, fewer Basic Sets can be made up than Regular Sets. This results in higher overall profit OC. Since the Regular Set requires more knives, it has higher production costs. This will result in less profit than the Basic Set. OD. The overall profit is most affected by the Deluxe Set. The profit generated by the Basic Set and Regular Set does not significantly contribute to the overall profit. An animal food must provide 54 units of vitamins and 59 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 & 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 X1 X2 54 55 2 2.5 5 1 000 4.5 3 0 1 0 10 0 0 1 0 10 0 000 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. When 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 decimal place as needed.) (b) What is the minimum cost? The minimum cost is cents. (Round to one decimal place as needed.)
