The simplex method can be used to solve the following linear programming problem.Minimize this function:C= 1000x + 1800y + 8000zSubject to these constraints:10x + 6y+20z ≥ 125x+10y + 50z ≥ 105x + 2y + 10z ≥ 5x = 0, y = 0, z ≥ 0IMinimum value of C =This value of C occurs when:X =y =Z=

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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#4 Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative.Maximize f = 6x + 9y + 6z subject to 4x + 7y + 9z ≤ 100 6x + 5y + z ≤ 135 x + 4y + 9z ≤ 30
olve the following linear programming problem using the Simplex method. Where: X1= Amount to invest in project A X2 = Amount to invest in product B Being the objective function: Xo = X1 + X2 (Maximize) Subject to: X1 + 2X2 ≤ 300 2 X1 + X2 ≤ 400 X1 + 2 X2 ≤ 400 X1, X2 ≥ 0
Day traders typically buy and sell stocks (or other investment instruments) during the trading day and sell all investments by the end of the day. The following table shows the closing prices on September 22, 2015, of 12 stocks selected by your broker, Prudence Swift, as well as the change that day. Tech Stocks Close Change AAPL (Apple) $113.40 -1.81 ADBE (Adobe Systems) $84.66 1.34 EBAY (eBay) $25.61 -0.31 MSFT (Microsoft) $3.90 -0.21 S (Sprint) $4.40 0.02 WIFI (Boingo Wireless) $8.51 0.56 Non-Tech Stocks ANF (Abercrombie & Fitch) $21.81 -0.02 в (Воeing) $133.99 -2.03 F (Ford Motor Co.) $13.91 -0.40 GE (General Electric) $25.10 0.01 GIS (General Mills) $57.12 0.33 JNJ (Johnson & Johnson) $93.26 0.13 On the morning of September 22, 2015, Swift advised you to purchase a collection of three tech stocks and two non-tech stocks, all chosen at random from those listed in the table. You were to sell all the stocks at the end of the trading day. (a) How many possible collections are possible?…
Minimise x2+y−2xyx2+y−2xy subject to the constraint y=1
Use the simplex method to solve the following linear programming problem. Find y₁ ≥0 and y₂ 20 such that 4y₁ + y₂ ≥6, y₁ + 4y₂ ≥6, and w=5y₁ +26y₂ is minimized. =aty₁ = [ The minimum is w = (Simplify your answers.) =and y₂ =.
Solve this linear programming problem using graphical methods. Restrict x ≥ 0 and y ≥ 0. Minimize g = x +9y, subject to the following. g= 8x + x + x + y ≥ 85 y≥ 50 4y2 80 x+10y 104
Formulate a linear programming problem that can be used to solve the following question. An individual needs a daily supplement of at least 380 units of vitamin C and 64 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 34 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 20 units of vitamin C and also 12 units of vitamin E. The total supplement of these two foods must be at most 29 ounces. Unfortunately, food I contains 22 units of cholesterol per ounce and food II contains 32 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. X = ---Select--- y = --Select--- ---Select--- | F = Subject to (objective function) (total ounces of food) (units of vitamin C) (units of vitamin E) x ---Select--- 0, y ---Select--- 0 (nonnegativity constraint)
Consider the problemMaximize z = x1 + 5x2 + 3x3subject tox1 + 2x2 + x3 = 62x1 - x2 = 8x1, x2, x3 >= 0The variable x3 plays the role of a slack. Thus, no artificial variable is needed in the firstconstraint. In the second constraint, an artificial variable, R, is needed. Solve the problemusing x3 and R as the starting variables.
Solve the following Linear Programming problem using graphical solution method: Minimize Z = 3X1 + 2X2 subject to 6X1 +4X2 = 24 X1 + X2 <= 5 X1 >= 3 X2 <=2 X1, x2 >= 0
Explain important characteristics of situations to which linear programming method can be successfully applied. Assume a suitable example A firm manufactures three products A, B, and Time to manufacture product A is twice that for B and thrice that for C and if the entire labour is engaged in making product A, 1,600 units of this product can be produced. These products are to be produced in the ratio 3:4:5. There is demand for at least 300, 250 and 200 units of products A, B and C and the profit earned per unit is sh. 90, sh. 40 and sh. 30 respectively. Table Raw material Requirement per unit of product (kg) Total availability (kg) A B C P 6 5 2 5,000 Q 4 7 3 6,000 Formulate the problem as a linear programming problem.

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