Given the following LP model and answer questions below: Max. 23X1+ 9X2 + 18X3+14X4 S.T: 5X1 +8X2 + 11X3 +6X4 = 30 17X1 +9X2 + 25X3 >= 40 10X1 + + 12X4<= 40 114X2 + 15X4<= 80 X1, X2, X3, X4 >= Zero 1. The slack/surplus variable for the constraints are: 2. If the profit/unit of X4 decrease to 8 JD, the value of the optimal solution will be: 3. If constraint (3) is modified to (>=), determine what will happen to the optimal solution: 4. If constraint (2) is modified to (<=), the binding constraints is/are:
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- minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2A simplex tableau is shown below. You should complete the tableau and respond to the questions posed. Basis CB cj JIN Cj Zj X1 3 1 X2 4 x3 0 0 5 1/2 0 1 S1 O 1/2 S2 O -1/2 6 -1/4 1 What is the current value of the objective function of the current simplex tableau? (round to 2 decimal places) 3Maximize p = 7x + 6y + 3z subject to x + y + z ≤ 150 x + y + z ≥ 100 x ≥ 0, y ≥ 0, z ≥ 0. p= (x, y, z)=
- LPP 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 )A mixture of pellets is to be made containing x regular pellets, y large pellets and z extra large pellets. Cost, weight and volume data for each type of pellet are shown in the table. Is it possible to make mixture of 55 pellets at a cost of $0.85 if the mixture is to have 120 weight units and 130 volume units? If so, how many each type of pellet should be in the mixture? Pellet Type 5. Number of Cost per Pellet in Cents Weight Units per Pellet Volume Pellets Units per Pellet Regular Large Extra large 2 1 4 y 1 4 3Minimization Case. Min C = X1 + X2 + X3Subject toX1 – 3X2 + 4X3 = 5X1 – 2X2 <= 32X2 + X3 >=0And X1, X2, X3 >= 0
- STAR Co. provides paper to smaller companies whose volumes are not large enough to warran paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The cutting patterns have been established: 1 2 Pattern 12ft. 15ft. 30ft. Trim Loss 0 4 1 10 ft. 3 0 7 ft. 8 0 0 4 ft. 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99 hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. hand will be sold on the open market at the selling price. No inventory is held. Number of: 3Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? A. Product_2 B. Product_1 C. Product_3 Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 13 5 $B$3 Product_2 175 0 25 8 9 $B$4 Product_3 0 −1.5 25 11 3 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 7003) Maximize Z= 2x, +x2 +3x 3 X+x2+2x3 <25 + X3 5 8 X2+ x3 S10 X1, X2, X3 2 0 Subject to IMe
- Determine the board measure (BF) and the cost 2x4 = $1700 MBM MBM or FBM = Thousand Board Measure or Thousand Board Feet 2 x 6 = $1600 MBM 2x10 = $ 1900 MBM 3/8 OSB = $ 1700 7/16 OSB = $ 1750 All prices are given is per Thousand Square Feet 3/4 OSB = $ 2400 1) 250 pcs of 2x4 …. 10 feet long 2) 300 pcs of 2x6 …. 4 meters long 3) 45 pcs of 2x10 …. 16 foot longXYZ Corporation manufactures two products, Simple and Complex. The following annual information was gathered: Simple Complex Selling price per unit P47.00 P26.00 Variable cost per unit 42.00 22.00 Total annual fixed costs are P18,000. Assume XYZ Corporation can produce and sell any mix of Simple or Complex at full capacity. It takes 1.5 hours to make one unit of Complex. However, Simple takes 50% longer to manufacture when compared to Complex. Only 120,000 hours of plant capacity are available. How many units of Simple and Complex should XYZ Corporation produce and sell in a year to maximize profits?XYZ Corporation manufactures two products, Simple and Complex. The following annual information was gathered: Simple Complex Selling price per unit P47.00 P26.00 Variable cost per unit 42.00 22.00 Total annual fixed costs are P18,000. Assume XYZ Corporation can produce and sell any mix of Simple or Complex at full capacity. It takes one hour to make one unit of Complex. However, Simple takes 50% longer to manufacture when compared to Complex. Only 120,000 hours of plant capacity are available. How many units of Simple and Complex should XYZ Corporation produce and sell in a year to maximize profits?