Solve the following linear programming problem graphically: Maximize Z=3X+5Y Subject to: 4X+4Y≤48 C₁ 1X+2Y=20 C₂ y22 C3 X, YZ0 1) Using the line drawing tool, plot constraint C₁ by picking two endpoints for the line. 2) Using the point drawing tool, plot the corner points which define the feasible region. 20+ 18- 16+ 14+ 12- 10- 8+ 6- 4- 24 X Objective functions X Q o 4
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- Using the grid technique to determine the least-cost location (warehouse) for this problem: Tons Rate X - Coordinates Y – Coordinates S1 200 0.5 2 14 S2 300 0.6 6 10 M1 100 1 2 2 M2 100 2 10 14 M3 100 1 14 18 M4 100 2 14 6 The Grid center coordination is ____ and _____ (round the results to 1 decimal place) Group of answer choices (9.9; 7.8) (5.5; 6.9) (8.7; 10.5) (10.5; 6.4) (9.9; 8.9)City government has collected the following data on annual sales tax collections and new car registrations: Annual Sales Tax Collections (in millions) 1.0 1.4 1.9 2.0 1.8 2.1 2.3 2.5 New Car Registrations (in millions) 10 12 15 16 14 17 20 22 Determine the following: Plot these data and decide if a linear model is reasonable. Using the results of part a., find the estimated sales tax collections if new car registrations total 25,000,000.Long-Life Insurance has developed a linear model that it uses to determine the amount of term life insurance a family of four should have, based on the current age of the head of the household. The equation is:y = 850 − .1xwherey = Insurance needed ($000)x = Current age of head of household a. Plot the relationship on a graph. b. Use the equation to determine the amount of term life insurance to recommend for a family of four if the head of the household is 30 years old.
- Ian Langella faces a decision how large his gasoline station should be. The annual returns wil l depend on both the size of his station and number of marketing factors related to the oil in dustry and demand for gasoline. Ian develop a careful analysis based on the following table: Size of first station Market condition Market conditon Market conditon Good Fair Poor Small 50,000 20,000 -10,000 Medium 80,000 30,000 -20,000 Large 100,000 30,000 -40,000 Very large 300,000 25,000 -160,000 Develop a decision table for this decisionGraph the feasible region for the system of inequalities. 5x+y< -3 x-y > 3Maximize 8x + 9y Subject to -- x + 2 y 0 a) Solve using simplex method
- Q2. Solve the given LP problem on the right by (LP): Max Z = 2X1 + 4X2 %3D using The Graphical Solution Method. a) Find the optimal solution, determine the solution type. b) Find the optimality range for the changes in the objective coefficient c2. c) Find the feasibility range for the changes in the Right Hand Side (RHS) of one st. 3X1 + 2X2 < 12 Xị + 2X2 s 8 2X1 + X2 2 2 X1, X2 2 0 of the binding constraints.In the past, Peter Kelle's tire dealership in Baton Rouge sold an average of 1,000 radials each year. In the past 2 years, 200 and 260, respectively were sold in fall, 340 and 300 in winter, 150 and 175 in spring, and 300 and 275 in summer. With a major expansion planned, kelle projects sales next year to increase to 1,200 radials. Based on next year's projected sales, the demand for each season is going to be (enter your responses as whole numbers): Season Fall Demand2. Consider the transportation problem having the following parameter table (M is a big positive number) Source Demand 1 12345 2 3 5 1 2 3 343800 13 14 4 18 3 0 130940 Destination 4 5 22 29 18 21 M 3 5 26M940 16 M 11 24 34 19 23 11 4 6 Supply 0 ooooo 0 6 0 0 36 28 0 5 6 2 56743 (a) Use the northwest corner rule manually to obtain a complete initial BF solution, also find the objective value for this solution. How many basic variables are there in this solution? (b) Use Vogel's approximation method manually to select the first basic variable for an initial BF solution. (Attention, do not need to find an complete initial BF solution, just find the first BV for this initial BF solution)
- In the past, Peter Kelle's tire dealership in Baton Rouge sold an average of 1,000 radials each year. In the past 2 years, 220 and 250, respectively were sold in fall, 360 and 320 in winter, 145 and 175 in spring, and 300 and 230 in summer. With a major expansion planned, Kelle projects sales next year to increase to 1,200 radials. Based on next year's projected sales, the demand for each season is going to be (enter your responses as whole numbers): Season Demand Fall nothing3. The Captain of a Cricket team has to allot 5 middle position to 5 batsmen. The average runs scored by each batsman at these positions are as follows Batting Positions III Batsmen II IV V P 40 40 35 25 50 27 50 42 30 16 25 R. 50 48 40 60 20 19 20 18 25 T 58 60 59 55 Find the assignment of batsmen to positions, which would give the maximum number of runs. If another batsman 'U' with the following average runs in batting positions as given below: Batting Positions: Average Runs: Is added to the team, should he be added to play in the team? If so, who should be replaced by him? II II IV V 45 52 38 50 49Below is a table that shows the Freshmen Enrollment of the New Texas Elementary School during the 1a Semesters of the past ten (10) Academic Years (AY), AY 2013-2014 2014-2015 2015-2016 2016-02017 2017-2018 Freshmen Enrollees AY 200 220 235 270 315 4. For the Weighted Moving Averages model, use: a weight of 0.40 for the most recent data; a weight of 0.35 for the second most recent data; and a weight of 0.25 for the third most recent data. You are the Principal of New Texas Elementary School. You are interested to know the forecast of freshmen enrolment for the next academic year (AY2023-2024), in order to plan ahead the necessary resources: faculty, classroom, library holdings, physical facilities, student services, furniture and fixtures, etc.). These are the requirements: AT 2013-2014 1. Calculate the forecast using 5 forecasting techniques/methodologies/models namely: Naïve Model, Unweighted and Weighted Moving Averages, Exponential Smoothing, and Time-Series Regression. Follow and…