#### Тема: Use graphical methods to solve the linear programming problem (140)?

The initial tableau of Simplex method consists of all the coefficients of the decision variables of the original problem and the slack, surplus and artificial variables added in second step (in columns, with P 0 as the constant term and P i as the coefficients of the rest of X i variables), and constraints (in rows). The C b column contains the coefficients of the variables that are in the base.

The last row is calculated as follows: Z j = Σ(C bi ·P j ) for i = 1..m, where if j = 0, P 0 = b i and C 0 = 0, else P j = a ij. Although this is the first tableau of the Simplex method and all C b are null, so the calculation can simplified, and by this time Z j = -C j.

As the independent terms of all restrictions are positive no further action is required. Otherwise there would be multiplied by "-1" on both sides of the inequality (noting that this operation also affects the type of restriction).

The inequalities become equations by adding slack , surplus and artificial variables as the following table:

Successive constructed tableaux in the Simplex method will provide the value of the objective function at the vertices of the feasible region, adjusting simultaneously, the coefficients of initial and slack variables.

In the initial tableau the value of the objective function at the O-vertex is calculated, the coordinates (0,0) correspond to the value which have the basic variables, being the result 0.

Type your linear programming problem below. (Press "Example" to see how to set it up.)

As the independent terms of all restrictions are positive no further action is required. Otherwise there would be multiplied by "-1" on both sides of the inequality (noting that this operation also affects the type of restriction).

The inequalities become equations by adding slack , surplus and artificial variables as the following table:

Big Hi! Solve the following Linear Programming Problem via the Simplex Method:? Help!! I need to know what the inequalities/equations are to set up this problem: Solve the following Linear Programming Problem via the Simplex Method: A city council is working with a hotel developer to build several hotels along its beach-front. The developer has three prototypes: a convention-style hotel with 500 rooms costing \$100 million, a vacation-style hotel with 200 rooms costing \$20 million, and a small hotel with 50 rooms costing \$4 million. The city council wants a total capacity of at least 3,000 rooms and has three other restrictions: • at most three convention-style hotels; • at most twice as many small hotels as vacation-style; and • at least a fifth as many convention-style hotels as vacation-style and small combined. How many hotels of each type should the council request in order to minimize cost? Let C = Convention-style Hotel → 500 rm costing \$ 100 Million V = vacation-style hotel → 200 rm \$ 20 million S = small hotel → 50 \$ 4 million CONDITIONS: 1. Capacity = 3,000 rooms 2. C ≤ 3 3. S = 2V 4. C = 1/5 (V + S) C + V + S = 3000 ← eq5 C = 3 ◄ No. of Convention Hotels From 4 C = 1/5 (V + S) 3 = 1/5 (V + 2V) 15 = 3V ================================== V = 5 ◄ No. of Vacation-style Hotels ================================== Substitute V to 3 S = 2(5) ============================== S = 10 ◄ No. of Small Hotels ============================== From eq5 C + V + S = 3000 3(500) + 5(200) + 10(50) = 3000 1500 + 1000 + 500 = 3000 3000 = 3000 ← Correct Cost C = 3 (100 m ) → \$ 300 m V = 5 (20 m ) → \$ 100 m S = 10 (4 m ) → \$ 40 m ========================== Total → \$ 440 million ========================== Hope this helps Remember that Jesus loves you. Know Him in His words the Bible. God Bless Lim♥E

If x, y and z are the quantities to be produced of items of types A, B, C, we ll have the following Linear Programming Problem: Maximize P = 24x + 10y + 20z, subject to 4x + 3y+ 5z ≤ 534; 2x + y + z ≤ 360; x ≥ 60; y ≥ 78; x, y, z - non-negative integers. The initial simplex tableau has 4 rows and 7+1 columns (4 constraints with 3 initial + 4 slick variables to equalize the inequalities + 1 column for the values). The optimal solution is Maximum_Profit = 2580, x = 75, y = 78 , z = 0 (no items of type C should be produced).