Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce O LaserStop models andO SpeedBuster models. This solution gives the possible profit, which is $ (Type integers or decimals rounded to two decimal places as needed.)
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- Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)Valencia Products makes automobile radar detectors and assembles two models: LaserStop and SpeedBuster. Both models use the same electronic components. After reviewing the components required and the profit for each model, the firm found the following linear optimization model for profit, where L is the number of LaserStop models produced and S is the number of SpeedBuster models produced. Implement the linear optimization model on a spreadsheet and use Solver to find an optimal solution. Interpret the optimal solution, identify the binding constraints, and verify the values of the slack variables. Maximize Profit = 123L+139S 17 L+11 S≤5000 (Availability of component A) 5L+9S≤4500 (Availability of component B) L≥0 and S≥0 Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce _ LaserStop models and _ SpeedBuster models. This…Valencia products makes automobile radar detectors and assembles two models. Laser stop and Speedbuster both models use the same electronic components after reviewing the components required and the profit for each model, the firm found the following linear optimization model for profit, where L is the number of LaserStop models produced and S is the number of Speedbuster models produced. Implement the linear optimization model on a spreadsheet and use. Solver to find an optimal solution. Interpret the optimal solution, identify the binding constraints and verify the values of the slack variables . Maximize profit = 123 L + 139 S 19 L + 11 S < 4,000 (availability of component A) 6 L + 9 S < 35000 (availability of component B) L > 0 and S > 0 The optimal solution is to produce how many Laser stop models ? And how many Speedbuster models ? The maximum possible profit is ? Component A is or is not a binding…
- Consider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0Company aims to determine the optimal number of products to be produced in order to maximize the total profit. a) Formulate the problem using algebraic method. b) Solve the model using the graphical method (indicate optimal solution and profit). C) again). Use graphical method to determine the shadow price for each of these resources (based on the definition of shadow price and by increasing each resource by one unit and solving the problem d) Use the Excel solver to do parts b and c. e) follow: Using Solver Table generate the optimal solution and the total profit for each resource as e1: Consider unit profit for product 1 (use range from 0 to 4 and increment of 1) e2: Consider unit profit for product 2 (use range from 0 to 4 and increment of 1) е3: Consider simultaneous changes for both unit profits in part e1 and e2 using given ranges. e4: Consider available resource of Raw material 1 (use range from 2 to 14 and increment of 1) e5: Consider available resource of Raw material 2 (use…Instructions: Solve using Excel Solver. Create the linear programming model and get the optimal solution to the problem. (Follow the steps and format in the photo below) 1. A company manufactures two products X1 and X2 on three machines A, B, and C. X1 requires 1 hour on machine A and 1hour on machine B and yields a revenue of Php 30. Product X2 requires 2 hours on machine A and 1 hour on machine B and 1 hour on machine C and yields revenue of PhP 50. In the coming planning period the available time of three machines A, B, and C are 2000 hours, 1500 hours and 600 hours respectively. Find the optimal product mix.
- Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?Solve the following linear programming problem graphically: Maximize Z=3X+5Y Subject to: 4X+4Y ≤48 C1 1X+2Y ≤20 C2 Y ≥2 C3 X, Y ≥0 Part 2 1) Using the line drawing tool, plot constraint C1 by picking two endpoints for the line. 2) Using the point drawing tool, plot the corner points which define the feasible region. The optimal solution is X= ____ and Y= _______ ( round your responses to whole numbers) Maximum Profit is $ _____ ( round your responses to whole numbers)1. True/FalseA company wants to hire 4 vendors for the sale of 4 products, they could only sell one type of product. The following table (image) indicates what each seller charges for selling each of the products. The company wants to assign each seller a product, find all possible optimal assignments by pinpointing their optimal cost. answer the following:a) It is an allocation model T() F()b) It is not a transportation model T() F()c) The model is not balanced T() F()d) The problem has exactly 24 feasible points T() F()
- Solve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Minimize z = x + y Subject to 4x + y ≥ 50 x + 4y ≥ 50 x ≤ 23 y ≤ 23 Minimum value is z = at(x, y) = ( , )A firm operates two types of machines A and B as shown in the table. Type A Type B Maximum Space Available Floor Space Available 3 2 18 Number of Workers 5 3 30 The ratio of machines of type A to those of type B should be greater than one. Tasks Define the term linear programming Write down four inequalities to represent the information above. If the profit from using type A machine is Shs 6000 per hour and that of B is Shs 9000 per hour, write down the expression for the profit in terms of and Find the number of machines of each type that should be in operation to give the maximum profit. Hence find the maximum profit What advice do you give to this company’s manager-For this problem clearly derive the Linear program-Graph this problem and clearly indicate the feasible options- Clearly determine the solution to the problem using the method of points (be smart about which points you have to evaluate based on the graph of the objective function