Solve the following LP optimization problem using the simplex method: maximize 40x + 30 subject to x + y <= 12, 2x + y <= 16 x >= 1 , y >= 0

Find an optimal Hoffman code for g:5, o:15, u:28, m:25, b:10, c:17. draw out steps so i can understand

Obtain the set of necessary and sufficient conditions for the following NLP Minimize Z = 2x - 24x1x2 + 2x% – 3x3 – 24x1x3 – 8x2x3 + 150

Q5/ by using Graphical Method to determine the optimal value of X1 & X2 that maximize value of Z. Max Z=5X1+ 7X2. Subject to: X1+X2 =0

Problem: Solve the following equality-constrained optimiza- tion problem using Newton descent algorithm with the initial point (1, 4, 0): min f(x, y, z) = e" + 2y? + 3z2 x,y,z subject to x – 5z = 1 | y + z = 4 Compute the optimal dual variables as well. You have to answered above problem By using Python Programming Language.

K = 0, L = 18 Write and solve the following linear program using lingo, take screen shots of your model as well as the reports and the optimal solution. Clearly show the optimal solution.NB:K=the second digit of your student number;L=sum of the digits of your student number, For example if your student number is 17400159 thenK=7andL=1+7+4+0+0+1+5+9=27!!!! SAVE YOUR FILE BY YOUR STUDENT NUMBER!!!!minz=t∈T∑​(At​Yt​+Pt​Xt​)+k∈K∑​(Hk​Uk​+Bk​Vk​)s.t.Uk​+Vk​=50∀k∈KXt​−Ct​Yt​<=0∀t∈Tk∈K∑​Vk​≥80t∈T∑​Xt​≥t∈T∑​Dt​Xt​>=0∀t∈TYt​∈{0,1}∀t∈TUk​>=0∀k∈KVk​>=0∀k∈KThe sets parameters and data are as follows: \[ \begin{array}{l} \mathrm{T}=\{1,2,3,4\} \\ \mathrm{K}=\{0,1,2,3,4\} \\ \mathrm{A}=\{5000,7000,8000,4000\} \\ \mathrm{D}=\{250,65,500,400\} \\ \mathrm{C}=\{500,900,700,800\} \\ \mathrm{P}=\{20, \mathrm{~L}, 25,20\} \\ \mathrm{H}=\{5,3,2, \mathrm{~K}, 9\} \\ \mathrm{B}=\{8,5,4,7,6\} \end{array} \]

Cse

HOMEPRO is a furniture manufacturer which produces two sizes of wood blocks (type A and B) thatare used to make either a table or a chair. A table is made of a type A and a type B wood blocks,while a chair is made of a type A and two type B wood blocks (See Figure 1) A table makes RM 3 profit, and a chair makes RM 5 profit. If M number of type A and Nnumber of type B wood blocks are produced, how many tables and chairs should themanufacturer make to obtain the greatest profit?For example, let M = 12 and N = 12.By making 4 tables (4 type A and 4 type B) and 4 chairs (4 type A and 8 type B), themanufacturer gain profit as follows,Profit = (RM 3) × 4 + (RM 5) × 4 = RM 32.If the manufacturer makes 2 more tables and 1 less chair, the profit will be increased as follows,Profit = (RM 3) × 6 + (RM 5) × 3 = RM 33.Is this the greatest profit? Write a complete C++ program to help the manufacturer determine the greatest profit obtainfrom making tables and chairs with a given number of M type A and…