In Exercises 1-8, write down (without solving) the dual LP problem. [HINT: See Quick Example 4.]
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- 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.arrow_forward3,2 3.2 X(x²-1)-y=xy ;y(2)=-arrow_forwardSection 2.6 1. Consider the production model x = Cx+d for an economy with two sectors, where =[0.6 0.5 0.2 and C 50 [30] (a) Determine the production level necessary to satisfy the final demand d. d = 1 (b) What is the production level to satisfy a final demand of (c) What is the production level to satisfy a final demand of 51 30arrow_forward
- Write down (without solving) the dual LP problem. Minimize c =s+6t+u 9s -t+v 23,000 u - v 21,000 subject to s+t2500 s20, t20, u 20, v 20arrow_forward2. The Minimum point of y= 8x+4 (x-2)²arrow_forwardConsider the LP model below. Use Branch and Bound to find the optimal solution. Маx z = 2x1 + x2 %3D subject to 10x1 + 9x2 s 8 8х1 + 6х2 2 1 X1, X2 2 0 and integersarrow_forward
- (2) Use the Two-phase method to solve the following LPP: maximize subject to -2 91 92 93 = 1 z ≥ 93 - 92 z = 91 92 91, 92, 93, z> 0arrow_forwardQ4. In simulation study of a manufacturing system, both the average daily production rates obtained from simulation model (use data from day n1/2 to day n2/2, round it to nearest integer) and from the real system are given, in data set 3. - n1= 6. , n2= 76 - Apply t test to decide if we can assume the simulation model is a valid representation of the real system is given. - Check if we can assume the average daily production rates obtained from simulation in successive days are independent by using scatter diagram (X Y plot in excel; X axis Xi value Y axis Xi+1)arrow_forwardWhich is a correct solution of y = 4x – 3? O (1, 3) O (1, 2) O (0, 1) O (2, 5)arrow_forward
- 7. Use Lagrange multipliers to give an alternate solution. Find two positive numbers whose product is 100 and whose sum is a minimum.arrow_forwardQ.4// Use Big-M method to solve the Mathematical model (Stop at Table 3) Max Z = x1+ 3x,+ 4x3+ 5 S.t. 4x1+ 3x2+ 2x3 +x4<10 X1-X3+2x4= 2 Xj+X2+X3+X421 X1 , X2 ,X3 , X420arrow_forwardA 2nd order homogenous LDE has a solution xe-3x Find its general solution.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning