Solve the following Linear Programming model using the graphical method (USING EXCEL) {Write the steps of construction} Q1) Maximize H = x + 3y Objective function subject to x + y ≤ 50 2x + y ≤ 60 x ≥ 0, y ≥ 0
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Solve the following Linear Programming model using the graphical method (USING EXCEL)
{Write the steps of construction}
Q1)
Maximize
H = x + 3y
Objective function
subject to
x + y ≤ 50
2x + y ≤ 60
x ≥ 0, y ≥ 0
Step by step
Solved in 2 steps with 3 images
- Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.Max Z = 3X1 + 4X2 Sub to: X1 + X2 ≤ 20 2X1 + 3X2 ≤ 50 And X1, X2 ≥ 0 (SOLVE MANUALLY USING SIMPLEX METHOD PLEASE DON'T USE SHORTCUTS)
- Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.Heller Manufacturing has two production facilities that manufacture baseball gloves. Production costs at the two facilities differ because of varying labor rates, local property taxes, type of equipment, capacity, and so on. The Dayton plant has weekly costs that can be expressed as a function of the number of gloves produced TCD(X) = X2 − X + 4 where X is the weekly production volume in thousands of units and TCD(X) is the cost in thousands of dollars. The Hamilton plant's weekly production costs are given by TCH(Y) = Y2 + 2Y + 3 where Y is the weekly production volume in thousands of units and TCH(Y) is the cost in thousands of dollars. Heller Manufacturing would like to produce 9,000 gloves per week at the lowest possible cost. (a) Formulate a mathematical model that can be used to determine the optimal number of gloves to produce each week at each facility. min s.t. = 9 X, Y ≥ 0 (b) Use Excel Solver or LINGO to find the…What is meant by parametric linear programming ?
- n using Excel to solve linear programming problems, the objective cell represents the a. value of the objective function. b. constraints. c. decision variables. d. total cost of the model.What function does linear programming play in OR?Find the indicated maximum or minimum value of the objective function in the linear programming problem. Minimize g = 10x + 6y subject to the following. x + 2y ≥ 10 2x + y ≥ 11 x + y ≥ 9 x ≥ 0, y ≥ 0