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Q1:1. As shown in the figure, a number of tanks are connected by pipes where, at steady state, the mass flow into and out of each tank must be equal. The rate of mass flow through each pipe is computed as the product of flow (Q) and concentration (c). As an example, the mass balance for the first tank can be written as, Q01 C01 Q31C3 = Q15C1 + Q12C1 Write mass balances for all the tanks and express the equations in matrix form. Then, use Matlab to solve for the concentrations in each tank. Q15 = 3 25 201 = 5 Q12=3 Col = 10 255 = 2 Qs4=2 Q24-1 244-11 Q23=1 24-8 Q = 1 203 = 8 C03 =20See Answer
Q2:Total budget is $4000 to spend. What is the best way to maximize profits out of the following items which need to fit on a 60" long by 30" wide table. SOLVE USING SIMPLEX METHOD Candles Cost: $4, sell $12 6" square space/unit Wigs Cost: $10, Sell for 30 10" square space/unit Hat Clips Cost: $10, Sell for $24 2" square space/unit I am pretty sure the answer comes out to 125 wigs, 275 golf clips and zero candles for standard profit maximizationSee Answer
Q3:1: Consider the following problems from the first homework. For each, derive the dual problem and illustrate that strong duality holds for these problems by finding the optimal solution to the dual (You need to find the values of the slack variables aswell!). (Hint: You do not need to use the simplex method for this problem)See Answer
Q4:4: Imagine you are a college student trying to live on a small budget. You want to minimize your food costs, but you know a diet consisting solely of instant ramen and beer may be harmful to your health. You look up recommended dietary allowance of several different nutrients to determine what you should eat to be healthy. Let i = 1...m denote the nutrients and let bi, i = 1...m denote the minimum daily requirement for each of the nutrients. Suppose make a list of your n favorite foods. Let j denote their index on your list and c; be the cost of the jh item. Let a denote the amount of the įth nutrient contained in the jth item on your food list. a: Formulate a linear problem to minimize your costs while still getting all of your daily required nutrients b: Formulate the dual to this problem c: Introduce another person to this story who is naturally interested in solving the dual problem. (Hint: Give semantic meaning to the dual problem) d: Name some real-world considerations that your model leaves outSee Answer
Q5:Green Grass, Inc. just ran out of stock and suddenly has two emergency orders for grass seed blends: one is for 1500 pounds of normal, the other for 2300 pounds of special. At least each pound of normal should contain 60 percent annual seed, while each pound of special should contain at least 70 percent perennial seed. Green Grass has two input mixtures, A and B. Mixture A contains 80 percent perennial and 15 percent annual seed. Mixture B contains 70 percent annual and 25 percent perennial seed. Mixture A costs 90 cents per pound and mixture B costs 50 cents per pound. Provide a complete LP formulation for this problem in the standard format. DO NOT SOLVE.See Answer

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