4X1 + 2X2 = 22; X1 – X2 = 4 1. Using Excel Graphics (Hint: Draw...
4X1 + 2X2 = 22; X1 – X2 = 4 1. Using Excel Graphics (Hint: Draw graphs representing the two equations for the range of values X1 = 0, 2, 4, 6, 8 and determine point of intersection from the graph) 2. Using Excel - Solver tools (Hint: Use DATA /ANALYSIS /SOLVER) 3. Using standard analytical techniques 4. (Bonus 5) Using Inverse Matrix and Matrix Multiplication techniques (Hint: MINVERSE and MMULT Excel functions)
Homework Answers
1. The intersection point is (5,1)
2. 
3. 
Remeber that for matrix the input is an array, so use CTRL+SHIFT+ENTER
Max 4x1 - 22 + 2.T3 Subiect to: 2x1 + x2 7 Min 4 + 2x2 - T3 Subject to: x1 + 2x2-6
Determine the Dual of the following Linear Programming
Problems
Max 4x1 - 22 + 2.T3 Subiect to: 2x1 + x2 7 Min 4 + 2x2 - T3 Subject to: x1 + 2x2-6
Max 4x1 - 22 + 2.T3 Subiect to: 2x1 + x2 7 Min 4 + 2x2 - T3 Subject to: x1 + 2x2-6
Incorporate this model into a spreadsheet using the picture below as a guide for the Excel spreadsheet you develop: (th...
Incorporate this model into a spreadsheet using the picture
below as a guide for the Excel spreadsheet you develop: (the unit
profit cells have been filled in for you to give you a start).
Hint: There are SUMPRODUCT functions in the two “Resource Used”
cells, and another SUMPRODUCT function in the “Total Profit”
cell.
Hint: to answer questions parts c, d,
and e, substitute each X1 and X2 values in parts c, d, and e below
into the constraints on...
1. Suppose U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and...
1. Suppose U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and m = 20. (15pts) a. Solve for the Utility maximizing amounts of x, and X2. b. Is this an interior or corner solution? c. Is the budget exhausted here? Yes/no d. Assume that the above prices and income have all doubled. How does this change your solution in a? e. Set up the Lagrangian for this problem (but do not solve it) 2. Suppose...
Your problem will have exactly two variables (an X1 and an X2) and will incorporate a maximization (either profit or revenue) objective. You will include at least four constraints (not including the X...
Your problem will have exactly two variables (an X1 and an X2) and will incorporate a maximization (either profit or revenue) objective. You will include at least four constraints (not including the X1 ≥ 0 and X2 ≥ 0 [i.e., the “Non-negativity” or “Duh!”] constraints). At least one of these four must be a “≤” constraint, and at least one other must be a “≥” constraint; do not include any “= only” constraints. You must have a unique Optimal Solution...
Determine the Dual of the following Linear Programming
Problems
Max 4x1 - 22 + 2.T3 Subiect to: 2x1 + x2 7 Min 4 + 2x2 - T3 Subject to: x1 + 2x2-6
Max 4x1 - 22 + 2.T3 Subiect to: 2x1 + x2 7 Min 4 + 2x2 - T3 Subject to: x1 + 2x2-6
Incorporate this model into a spreadsheet using the picture
below as a guide for the Excel spreadsheet you develop: (the unit
profit cells have been filled in for you to give you a start).
Hint: There are SUMPRODUCT functions in the two “Resource Used”
cells, and another SUMPRODUCT function in the “Total Profit”
cell.
Hint: to answer questions parts c, d,
and e, substitute each X1 and X2 values in parts c, d, and e below
into the constraints on...
1. Suppose U(X1, X2) = 2lnx, + 3lnx, and P, = 4, P2 = 1, and m = 20. (15pts) a. Solve for the Utility maximizing amounts of x, and X2. b. Is this an interior or corner solution? c. Is the budget exhausted here? Yes/no d. Assume that the above prices and income have all doubled. How does this change your solution in a? e. Set up the Lagrangian for this problem (but do not solve it) 2. Suppose...
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