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- Maximize profit = 4X + 4Y Subject to: 3X +5Y ≤ 150 X – 2Y ≤ 10 5X + 3Y ≤ 150 X, Y ≥ 0 Required: a- The corner point method to obtain the optimal point. b- Specify the profit value. c- Calculate the Slack for each constraint and state its formula.Discuss the five (5) steps of the Theory of Constraints and apply each to asimulation/assumption of a constraint impacting Jaguar.Formulate the Linear Programming algebraic model : The DLSU Faculty Cooperative has P250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return of 9%. Cooperatives regulations require diversification to the extent that at least 50% of the investment be placed in Treasury notes. Because of restrictions of Bureau of Internal Revenue, it is decided that no more than 40% of the investment be placed in bonds. Determine the budget that should be allocated
- Problem 8-21 (Algorithmic) Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Rental Class Room Super Saver Deluxe Business Type I $30 $35 — Type II $20 $30 $40 Type I rooms do not have wireless Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be…Don't solve. Please give- Decision Variable Constraint Objective function#5) Solve the following LP a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if the profit for oak tables increases to $83? c) What is the optimal solution and objective function value if the profit for pine chairs decreases to $13? d) What is the optimal solution and objective function value if the profit for pine tables increases by $20? e) What is the optimal solution and objective function value if the company is required to make at least 20 pine chairs? f) What is the optimal solution and objective function value if the company is required to make no more than 55 cherry chairs?
- Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 13x + 3y + 12z 6x + 14y + 21z 2 66 15x + 20y + 7z 2 132 x 2 0, y ż 0, z ż 0. subject to and a. What is the optimal value of x? b. What is the optimal value of y? c. What is the optimal value of z? d. What is the minimum value of the objective function?Please define the decision variables, define the objection function & define the constraintssolve for the range of optimality, asap thank you
- What is the best choice of the crop given a constraint of 1000 acres?Formulate and prove a sufficient condition for optimality for an infinite-horizon problem.Variable Cells Model Variable W M Constraints Constraint Number 1 2 3 Name Westem Foods Salsa Mexico City Salsa Name Whole tomatoes Tomato sauce Tomato paste Final Value 560.000 240.000 Reduced Objective Cost Coefficient 0.000 1.000 0.000 1.250 Shadow Price Final Value 4480,000 1920,000 1600,000 0.188 0.125 0,000 Constraint R.H. Side 4480.000 2080.000 1600,000 Allowable Increase 0.250 0.150 Allowable Increase 1120.000 1E+30 40,000 Allowable Decrease 0.107 0.250 Allowable Decrease 160.000 160,000 320.000 Analyze the sensitivity report shown above- a. What is the optimal solution and what are the optimal production quantities? b. Specify the objective coefficient ranges. c. What are the shadow prices for each constraint? Interpret each. d. Identify each of the right-hand-side ranges