Solve the below Linear program and find the optimal solution from the below options: Minimize z = 2x 1 +3x 2 Subject to x1+x 2 ≥ 6 7x 1 +x2 > 14 x 1 and x 220
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- 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?Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.Q1 Find the best solution for the following model using simplex MAX Z = 10X1 + 8X2 SUB TO: 4X1 + 2X2 < 80 X1 + 2X2 < 50 X1 2 0,X2 2 0
- What combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: Multiple Choice x= 0, y=4 x= 0, y=3 x= 0, y=0 x= 2y=0 O x=1,y=25 2x + 4y ≤ 12 5x + 2y ≤ 10Solve the following problem using Simplex Method and find the P value. Maximize: P = 3x + 4y subject to: x+ y 03) Maximize Z= 2x, +x2 +3x 3 X+x2+2x3 <25 + X3 5 8 X2+ x3 S10 X1, X2, X3 2 0 Subject to IMe
- Solve the linear programming problem by the method of corners. Maximize P= x + 6y subject to x + y s4 2x + y s6 x 2 0, y 20 The maximum is P = at (x, y) = Need Help? Read ItLPP Model Maximize P = 12x + 10y Subject to : 4x + 3y < 480 2x + 3y < 360 X, y 2 0 Which of the following points (x, y) is feasible? A) ( 120, 10) B ( 30, 100 ) c) ( 60, 90 ) D) ( 10, 120 )Multiple Optimal Solution: Example (9): Find the optimal solution for the : Multiple Optimal following model by the graphical method Max Z = X,+X, X, +X, 23 .(1) X, +X, 56 S. to : X,21 ..(2) .(3) X, s2 (4) X, 20 X, 20
- FIND THE OPTIMUM SOLUTION TO X= Y= MAX Z=Graph the feasible region for the system of inequalities. 5x+y< -3 x-y > 3Solve the following Linear Programming model using the graphical method (USING EXCEL){Write the steps of construction} Q1)MaximizeH = x + 3y Objective functionsubject tox + y ≤ 502x + y ≤ 60 x ≥ 0, y ≥ 0