Solve using the simplex method the following problem: Maximize Z=3X1 + 2X2 subject to: 2X1+ X2 ≤ 18 2X1 + 3X2 ≤ 42 3X1 + X2 ≤ 24 X1 ≥ 0 , X2 ≥ 0

Consider the following nonlinear program. max x(y – 2) s.t. x = 33 - 3y y 2 2 (a) (b) Derive the KKT necessary conditions for the nonlinear Solve the nonlinear program using the KKT necessary conditions. program.

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).

Which of the folowing linear programming model has an unbounded feasible region? = 3x + 2y subject to the following : O max z x+ y34 *< 10 – 4y x20 y20 O None of the above O max z = 3x + 2y subject to the following : x+ 2y <4 x- ys1 x20 y20 O max z = 4x +2y subject to the following : x + 2y 24 3x + y27 -x + 2y s7 x20 y20

What is the algebraic formulation for this question, including objective function and constraints

eBook 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: Room Type 1 Type II Rental Class Super Saver $37 $18 Explain. Deluxe $40 $33 Variable SuperSaver rentals allocated to room type I SuperSaver rentals allocated to room type II Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II Business rentals allocated to room type II Is the demand by any rental class not satisfied? Business Type 1 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 125 rentals in the Super Saver…