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Given below are 2 consecutive simplex tables for an LPP in the maximisation form.Determine the values of the unknowns a,b,c,d,e,f,g.Also check if the solution corresponding to the second table is optimal.
Variables in
the basis A_1 A_2 A_3 A_4 Solu
x_3 1 2 1 0 8
x_4 2 1 0 1 10
∆_j -4 a 0 0 0

Variables in
the basis A_1 A_2 A_3 A_4 Solu
x_2 e 1 1/2 0 b
x_4 f 0 -1/2 1 c
∆_j g 0 3 0 d
show that for a transportation problem if the availability and requirement are in integer units then any basic feasible solution obtained by the transportation algorithm is also and integer factor.
The advertising director a large retail store in Columbus, Ohio, is considering three advertising media possibilities: (1) ads in the Sunday Columbus dispatch newspaper, (2) ads in a local trade magazine that is distributed free to all houses in the city and northwest suburbs, and (3) ads on Columbus’ WCC-TV station. She wishes to obtain a new customer exposure level of at least 50% within the city and 60% in the northwest suburbs. Each TV ad has a new-customer exposure level of 5% in the city and 3% in the northwest suburbs. The dispatch ads have corresponding exposure levels per ad of 3.5% and 3%, respectively, while the trade magazine has exposure levels per ad of 0.5% and 1%, respectively. The relevant costs are $1,000 per dispatch ad, $300 per trade magazine ad, and $2,000 per TV ad. The advertising policy is that no single media type should consume more than 45% of the total amount spent. Find the advertising strategy that will meet the store’s objective at minimum cost.
Solve the following linear program using SIMPLEX algorithm: (10)
Minimize z = a + b + c
Subject to: 1. a - b - c >= 0
2. a + b + c ≥ 4
3. a + b - c = 2
4. a, b >= 0
1.4 Given the constraints (10)
A+B + C <= 24, B +C >=8 and A >= 0, B >= 0, C>=  0.
Maximize 24-A-B - C
A: amount of time spent on school work
B: amount of time spent on fun
C: amount of time spent on pay work
Maximize z=3a+b+2c
Subject to: a + b+ 3c <=30, a>=0, b>=0, c>=0.
Maximize z = 3a + b + 2c
Subject to: 1. a + b + 3c <= 30
2. 2a + 2b + 5c<=  24
3. 4a + b + 2c<=  36
4. a,b,c>=  0
NB : a= Computers b= Network devices c= IP cameras
Z= Performance
-Numbers are costs.
The problem above consist of maximizing the performance of our computer network by reducing
the total cost.
Which of the following statements true or false? Give a short proof or a counter example
in support of your answers.

i) The forward and backward recursive formulation in Dynamic programming techniques can result in different optimum solutions to the same problem.

ii) A non-critical activity cannot have zero total float.

iii) The addition of a consultant to all the elements of an assignment problem can affect
the optimal solution of the problem.

iv) If the primal LPP has an unbounded solution, the dual LPP cannot have a feasible

v) In queuing theory, if the arrivals are according to Poisson distribution with parameter
λ , the inter-arrival time is exponential with parameter e^λ
a) A Company has factories at A, B and C which supply warehouses at D, E and F. Weekly factory capacities are 200, 160 and 90 units. Weekly warehouse requirements (demand) are 180, 120 and 150 units respectively. Unit shipping costs (in kshs) are as follows

Factory D E F Capacity
A 16 20 12 200
B 14 8 18 160
C 26 24 16 90
Demand 180 120 150 450
Draw the transportation tableau and show whether it is a degenerate or a non-degenerate problem.
The Make-It-Good manufacturing company produces three products, Widgets, Mingets, and Tringles.

During a given year they plan to produce a total of 13,000 units of these products.

The per unit production costs for Widgets, Mingets, and Tringles are $4, $5, and $7 respectively.

The per unit profit for the Widgets, Mingets, and Tringles is $1, $2, and $3 respectively.

If the production costs are to be $70,000 and the desired profit is $27,000, how many of each product should the company produce?

Set up the solution: define variables and determine the equations. Then, solve the system of equations using any valid method, and answer the question asked in the problem.
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