1.plot all the corner points for the feasible area. 2. Find the optimum solution to X= Y= VALUE Z=
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Example 14c
1.plot all the corner points for the feasible area.
2. Find the optimum solution to
X=
Y=
VALUE Z=
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- May I have the linear programming graph (or model) or plot with the given following information? 3 variables and 8 contraints Objective - Zmax = 1.85R+2.1D+2.15H Constraints: 0.15R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.15H ≤ 7500 0.25R + 0.2D + 0.15H ≤ 7500 0.10R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.20H ≤ 7500 R ≥ 10000 D ≥ 3000 H ≥ 5000Task 4In this task, you are asked to formulate the linear programming problem below andthen solve it.A carpenter produces Tables (T) and Chairs (C).Each Table unit requires 6kg of wood and 1kg of plastic.Each Chair unit requires 4kg of wood and 4kg of plastic.The carpenter has only 100kg of wood and only 50kg of plastic in stock.On each sale, the carpenter makes a profit of £15 per Table unit sold and a profit of£30 per Chair unit sold.Required:Formulate the Linear Programming problem above by defining the variables,stating the object function and the constraints.You are required to produce the graph for all inequalities (copy image to Word)Find the quantity to make of Tables and Chairs to maximise profit.21. A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is TRUE? Part 2 A. The graphical origin (0, 0) is not in the feasible region. B. The feasible region includes all points that satisfy one constraint, the other, or both. C. The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized. D. The two corner points are (0, 0) and (50, 12.5). E. There are four corner points including (50, 0) and (0, 12.5)
- Find the minimum value of the function z=2x+2y subject to the following constraints. x≤17 y≤16 5x+2y≥42 3x+11y≥84Let x = pieces of sofa, Y=pieces of table, Z=pieces of chair1.What is the objective function?2. Express the first constraint (wood) in mathematical sentence3. Express the second constraint (upholstery) in mathemathical sentence.4. Express the third constraint (Labor) in mathemathical sentenceConsider 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.
- 19. What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (1) 2x + 3y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x, y ≥ 0. Part 2 A. x = 0, y = 3 B. x = 2, y = 0 C. x = 0, y = 0 D. x = 0, y = 4 E. x = 1, y = 5Show the complete Linear Programming Model. Show solutions (i.e. decision variables, objective function, subject to constraints, etc.) Q. A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $1,000 per ton to process, and ore from source B costs $500 per ton to process. Costs must be kept to less than $4,000 per day. Moreover, Government Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? Formulate the LP model.do not need to solve thr problem, jsit crrate the linear program.
- Given the region of feasible solutions with corner points of (0,3), (4,2), (6,3), and (6,6), find the corner point that would minimize the objective function z = x +10y and state the minimum. Question 3 options: 66 3 24 36You own wheat warehouse with capacity of 20,000 bushels. At the beginning of month 1, you have 6,000 bushels of wheat. Each month, wheat can be bought and sold at the price per 1000 bushels given in the table Month Selling price ($) Purchase prie ($) 1 3 8 2 6 8 3 7 2 4 1 3 5 4 4 6 5 3 7 5 3 8 1 2 9 3 5 10 2 5 The sequence of events during each month is as follows: a. You observe your initial stock of wheat. b. You can sell any amount of wheat up to your initial stock at the current month's selling price. c. You can buy(at the current month's buying price) as much wheat as you want, subject to the warehouse size imitation. Your goal is to formulate an LP that can be used to determine how to maximise the profit earned over the next 10 months and solve using Excel solver or AMPLou are given a linear programming problem. Maximize P = 3x + 3y subject to 5x + 3y ≤ 30 Resource 1 2x + 3y ≤ 21 Resource 2 x ≤ 4 Resource 3 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1.