linear programming

A cargo airplane operated by has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space, as summarized below: Compartment Weight Capacity (tons) Space Capacity (cu.ft.) Front Center Back 12 13 10 7,000 9,000 5,000 To ensure proper weight and balance, the weight of the cargo in the respective compartments must be the same proportion of that compartment’s weight capacity. The following four cargos have been offered for shipment on an upcoming flight as space is available: Cargo Weight (tons) Volume (cu.ft./ton) Profit ($/ton) 1 2 3 4 20 16 25 13 500 700 600 400 280 360 320 250 ... click for more

Linear Programming - Simplex Methods (Finite Mathematics)

1. The feasible set of a certain linear programming problem is given by the following system of linear inequalities. x + 3y (less than or equal to symbol) 6 x - y (less than or equal to symbol) 2 - 5x + y (less than or equal to symbol) 2 Without graphing this set, determine which of the following points is not in the feasible set: a. (3,1) b. (1,1) c. (-1,2) d. (0,0) e. all of the above 2. A certain linear programming problem has the feasible set: x + 2y (less than or equal to symbol) 6 x - y (greater than or equal to symbol) 5 x (less than or equal to symbol) 3 Wh... click for more

Linear Programming : Simplex Method, Pivoting and Maximizing Values

1. Consider the following linear programming problem: Maximize 10x + 7y subject to: X + 3y (less than or equal to symbol) 10 2x -y (less than or equal to symbol) 8 x (greater than or equal to symbol) 0, y (greater than or equal to symbol) 0 The initial simplex tableau is: (for choices, please see attachment) 2. The particular solution corresponding to the simplex tableau (see attachment) is: a. x = 2, y = 6, u = 10, v = 0, M = 0 b. x = 2, y = 6, u = 0, v = 0, M = 10 c. x = 6, y = 0, u = 2, v = 0, M =10 d. x = 6, y = 0, u = 6, v = 0, M = 10 e. none of the above 3. The result of pivoting the simplex tableau (see attachment) about -2 (1st row, 1st colum... click for more

Solve a system of 3 equations.

solve for x(1), x(2), x(3); 1. 27,954.606 x(1) + 11,969.843 x(2) - 7515.1688 x(3) = 6124.3394 2. 11,969.843 x(1) + 5900.332 x(2) - 3586.4121 x(3) = 3054.3092 3. -7515.1688 x(1) - 3586.4121 x(2) + 2513.4532 x(3) = -1756.4525

Linear Programming : Find Optimal Solution

A businessman is considering opening a small specialized trucking firm. To make the firm profitable, it is estimated that it must have a daily trucking capacity of at least 84,000 cu. ft. Two types of trucks are appropriate for the specialized operation. Their characteristics are as follows: Truck Cost Capacity(Cu. ft) Drivers needed small $18,000 2,400 1 large $45,000 6,000 3 Note that the truck 2 requires 3 drivers for long haul trips. There are 41 potential drivers available and there are facilities for at most 40 trucks. The businessman's objective is to minimize the total cost outlay for trucks... click for more