Solve this using the graphical method. Be sure to clearly show all steps: Sketch the feasible region Determine the corner points Determine the minimum of the objective function ●
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- graph the following constraints: x + y <= 60 15x + 30y <= 20 0.9y > = 0.10x x > = (2/3) y Explan in detail19. What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (1) 2x + 3y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x, y ≥ 0. Part 2 A. x = 0, y = 3 B. x = 2, y = 0 C. x = 0, y = 0 D. x = 0, y = 4 E. x = 1, y = 5Solve 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
- L.P. Model: Maximize Z= 8X+2Y Subject to: 1X+2Y≤6 (C1) 5X+1Y≤20 (C2) X,Y≥0 On the graph on right, the constraints C1 and C2 have been plotted. Using the point drawing tool, plot the four corner points for the feasible area. The optimum solution is: X = (round your response to two decimal places). Y = (round your response to two decimal places). Optimal solution value Z = (round your response to two decimal places).Mr Sng is a retiree in his late sixties. He has $100,000 to invest. He has no regular source of income and no other assets. He is evaluating between 3 different lump-sum financial products shown in Table 3. All products require a minimum investment sum of $100,000. Monetary returns represent the net gain after one year of investing in the product. For example, if Mr Sng chose to invest in Product B, he may lose $5,000 after one year if the GDP growth is negative. He will earn $8,000 if the GDP growth exceeds 2% at the end of the year. If you were in the shoes of Mr Sng, how would you select the appropriate investment product for a time horizon of one year? (i) Use the Optimistic, Conservative and Regrets payoff analysis approaches. State which product(s) Mr Sng should invest in and what monetary return he can expect from each approach (ii) As you have only enough funds for one product, identify the most appropriate investment product. [Hint: Be sure to consider the…Maximization(Don't use excel shortcut solve manually by Simplex LPP method)1) Max Z = 3X1 + 4X2Sub toX1 + X2 ≤ 202X1 + 3X2 ≤ 50And X1, X2 ≥ 0
- Consider a long roll of wallpaper that repeats its patternevery yard. Four sheets of wallpaper must be cut from theroll. With reference to the beginning (point 0) of thewallpaper, the beginning and end of each sheet are locatedas shown in Table 78. Thus, sheet 1 begins 0.3 yd from thebeginning of the roll (and 1.3 yd from the beginning of theroll) and sheet 1 ends 0.7 yd from the beginning of the roll(and 1.7 yd from the beginning of the roll). Assume we are at the beginning of the roll. In what order should the sheetsbe cut to minimize the total amount of wasted paper?Assume that a final cut is made to bring the roll back to thebeginning of the pattern.Let: X1=x and X2=y Let profit=z Refer to the image: 1. What is the value of Y? 2. What are the three constraints?Perdaris Enterprises had an expenditure rate of E′(x) = e0.1x dollars per day and an income rate of I′(x) = 98.8 - e0.1x dollars per day on a particular job, where x was the number of days from the start of the job. The company’s profit on that job will equal total income less total expenditures. Profit will be maximized if the job ends at the optimum time, which is the point where the two curves meet. Find the following.(a) The optimum number of days for the job to last(b) The total income for the optimum number of days(c) The total expenditures for the optimum number of days(d) The maximum profit for the job
- A blueprint of a gallery with eight rooms, one entrance and thirteen doorways is shown. The gallery is laid out in a grid of three columns and four rows. Some rooms take up more than one row. The left-hand side contains rooms 1 and 2, the middle column rooms 3, 4, 5, and 6, and the right-hand side rooms 7 and 8. The following list contains each doorway and the rooms it connects. Entrance: Room 1 Opening 1: Rooms 1 and 3 Opening 2: Rooms 3 and 7 Opening 3: Rooms 3 and 4 Opening 4: Rooms 1 and 4 Opening 5: Rooms 4 and 7 Opening 6: Rooms 1 and 2 Opening 7: Rooms 4 and 5 Opening 8: Rooms 2 and 5 Opening 9: Rooms 5 and 7 Opening 10: Rooms 5 and 6 Opening 11: Rooms 7 and 8 Opening 12: Rooms 2 and 6 Opening 13: Rooms 6 and 8 A security firm proposed that two-way cameras be installed at some room openings. Each camera has the ability to monitor the two rooms between which the camera is located. For example, if a camera were located at opening number 4, rooms 1 and 4 would be…Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.Maximize z= 5R+8P Subject to R+3/2P≤900 1/2R+1/3P≤300 1/8R+1/4P≤100 R,P ≥ 0 non-binding constraint: R+(3/2) P≤900 binding constraints: (1/8) R+(1/4) P≤100 and (1/2) R+(1/3) P≤300 redundant constraint R+(3/2) P≤900 1. What is the range of the coeficient, c1, of the decision variable R that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2 2. What is the range of the coeficient, c2, of the decision variable P that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2