5. Consider the following LP:Minimize z = 7x1 + 15x2 + 20x3, subject to the constraints2x1 + 4x2 + 6x3 ≥24,3x1 + 9x2 + 6x3 ≥30,x1, x2, x3 ≥0.a) Solve the given LP using big M method
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5. Consider the following LP:
Minimize z = 7x1 + 15x2 + 20x3, subject to the constraints
2x1 + 4x2 + 6x3 ≥24,
3x1 + 9x2 + 6x3 ≥30,
x1, x2, x3 ≥0.
a) Solve the given LP using big M method
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- O Use the simplex method to find the maximum value of Maximize, Z = 20x1+10x2 subject to 4x1 + x2 + x3 = 30, 2x1 + 3x2 + x3 0.Find the maximum value of Q(x) = -2x + 10x3+4x1x2 subject to the constraint x² + x3 = 1. answer correct to 2 decimalsSolve min x1-x2-2x3 problem by means of Lagrange multipliers under the constraints of x1+x2+x3=5 and x12+ x22 =4. Explain what the values of Lagrange multipliers mean?
- A company manufactures two types of bicycles, a racing bicycle and a mountain bicycle. The total revenue (in thousands of dollars) from x1 units of racing bicycles and x2 units of mountain bicycles is R = −6x21 − 10x22 − 2x1x2 + 32x1 + 84x2 where x1 and x2 are in thousands of units. Find x1 and x2 so as to maximize the revenueSolve the following LPP using Simplex method Max P = 4X₁ + 3X2 + 4X3 + 6X4 Subjected to X₁ + 2X2 + 2X3 + 4X4 2X1+ 0X2 +2X3 + X4 -3X₁-3X₂ X3 - X4 = -80 Where X₁, X2, X3, X4 >= 0Q3/ Use the graphical method to solve the following LP problem. Minimize Z=-x₂ + 2x₂ subject to the constraints (1)-x₂ + 3x₂ ≤ 9 (11) x₂ + x₂ ≤ 6. (11)x₁-x₂54 and
- Solve the following LPP by graphical method : Maximize Z = 22x1 + 18x2 Subject to constraints: 960x1 + 640x2 ≤ 15360 x1 + x2 ≤ 20 and x1 , x2 ≥ 0Q2) Solve the following problem using the simplex method: Maximize: z = 4x+3y x +3y < 3 -2x +ys 5 X20, y 20Maximize P=3x1+4x2−5x3, Subject to: 2x1−3x2+2x3 ≤4 x1+2x2+4x3 ≤8 x2−x3 ≤6 x1,x2,x3 ≥0 and give the maximum value of P to the nearest integer.
- Q3- Find the optimum values of X1, X2 and X3 that maximize the values of Z using simplex method? Maximize Z= 3X1+ 4X2+X3 Subject to 3X1 +10X2 +5X3 <120 5X1 +2X2 +8X3<6 4X1 +10X2 +3X3 < 105 X1,X2,X3 >01. Ten year old Kayla's lemonade stand has experienced rises and falls in sales caused by temperature changes over the last few weeks. Her sales over the first few weeks of the summer were stacked according to the model S(x) =2x³ – 32x2 + 128x + 6 , where x is the number of weeks and S(x) is the number of sales. a) Kayla makes a profit if she sells at least 6 glasses of lemonade. Use the model to determine the number of days that she made a profit. b) What are the domain and range? Interpret each. c) Predict the number of sales on her last week of sales (Assume 12 weeks). Does this seem reasonable? What kind of conclusions would you make about the weather with this model?Use Lagrange multipliers to find three positive numbers whose sum is 110 and whose product is maximum. (Enter your answers as a comma-separated list.)
