With reference to the solution of LPP simplex method table when do you Conclude as follows : LPP has no limit for the improvement of objective function. LPP has no feasible solution
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- With reference to the solution of the LPP simplex method table, when do we Conclude that LPP has no limit for the improvement of the objective function?For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. i.e: Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) A construction company manufactures bags of concrete mix from beach sand and river sand. Each cubic meter of beach sand costs ₽60 and contains 4 units of fine sand, 3 units of coarse sand, and 5 units of gravel. Each cubic meter of river sand costs ₽100 and contains 3 units of fine sand, 6 units of coarse sand, and 2 units of gravel. Each bag of concrete must contain at least 12 units of fine sand, 12 units of coarse sand, and 10 units of gravel. Find the best combination of beach sand and river sand which will meet the minimum requirements of fine sand, coarse sand, and gravel at the least cost.For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) A farmer has 5 hectares of land to plant with rice and corn. He needs to decide how many hectares of rice and corn to plant. He can make ₽200,000 profit per hectare planted to rice and ₽250,000 profit per hectare planted with corn. However, the corn takes 2 hours of labor per hectare to harvest and the rice takes 1 hour per hectare. The farmer has 8 hours of labor to harvest. To maximize his profit, how many hectares of each should he plant? *additional note: philippine peso is used as currency :)*
- Consider the following LP problem with two constraints: 32X + 39Y >= 1248 and 17X + 24Y >= 408. The objective function is Max 13X + 19Y . What combination of X and Y will yield the optimum solution for this problem? a. 0 , 17 b. unbounded problem c. 0 , 17 d. infeasible problem e. 24 , 0Solve the following linear programming problem using simplex method. A printing company makes three grades of wall posters. The better-quality posters sell for Rs. 2.50, intermediate quality for Rs.2.00 and the poorer quality poster for Rs. 1.50. Paper costs Rs. 0.75 for each of the better-quality posters and Rs.0.50 and Rs. 0.25 for each intimidates and poorer quality poster respectively. Because of poor quality paper, the less expensive posters require two minutes of printing time while the other two require 1 minute of printing time only. The department is allocated Rs.150 per day for paper. There are 480 minutes of printing time available daily and each minute that is used to estimate to cost the company Rs. 0.25. In addition, the department incurs a fixed daily cost of Rs. 125, which are not affected by the quantity and quality of papers produced. You are asked to suggest as to how much each type of posters is to produce in order to maximize daily profit?The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 6x1 + 3x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 (a) Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ------ to -------- (b) Over what range can the coefficient of x2 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ----- to -------- (c) Compute the dual value for the first constraint, second constraint & third constraint
- The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 3x1 + x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) Compute the dual value for the third constraint.Canine LLC makes two types of dog food: Formula S and Formula X. They use linear programming model to determine the optimum mix of dog food to produce. The model they use is given below: Maximize: 50S + 60X Subject to these constraints: 8S + 10X ≤ 800 S + X ≤ 120 4S + 5X ≤ 500 S, D ≥ 0 Based on the information given above, the maximum value of the confectioner's linear programming is $_______.A healthy diet contains m different nutrients in quantities at least equal to b1, · · · , bm. This diet can be composed by choosing nonnegative quantities x1, · · · , xn of n different foods. One unit quantity of food j contains an amount aij of nutrient i, and has a cost of cj. Formulate this problem as an optimization problem in order to determine the cheapest diet that satisfies the nutritional requirements. What if we want to determine the most nutritious diet that does not exceed the cost given by the different foods? What is the relation between both formulations?
- suppose a linear programming (maximation) problem has been solved and that the optimal value of the objective function is $300. Suppose an additional constraint is added to this problem. Explain how this might affect the optimal value of the objective function.A Linear programming problem has the following three constraints: 30X + 14Y <= 420; 18X + 8Y= 144; and 19X - Y <= 67 . The objective function is Min 22X + 20Y . What combination of X and Y will yield the optimum solution for this problem? a. 0 , 18 b. unbounded problem c. infeasible problem d. 8 , 0 e. 4 , 9use the simplex method to solve the given linear programming problem (In each case the objective function is to be maximized.) Objective function: z = x_{1} - x_{2} + 2x_{3} Constraints: 2x_{1} + 2x_{2} <= 8 x_{3} <= 5 x_{1}, x_{2}, x_{3} >= 0