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A company manufactures two (2) electronic devices A and B. Each unit of device A requires 3 motors and 2 transformers, and each unit of device B requires 2 motors and 4 transformers. The supply of motors and transformers each day are limited to 2100 and 3000 units, respectively. Device B is a special model that comes with remote control, and the supply of remote control is limited to 650 units a day. The company gets a profit of RM 20 for each unit of device A and RM 30 for each unit of device B.

(a) If x represents the number of device A and y represents the number of device B that can be produced in a day, formulate the problem above in mathematical model.  

(b) By letting to represent the number of device A and to represent the number of device B that can be produced in a day, modify and convert the mathematical model in (a) into its standard form.   

(c)Solve the problem using Simplex Method.      

Four companies viz. W, X, Y and Z supply the requirements of three warehouses viz. A,

B and C respectively. The companies’ availability, warehouses requirements and the unit

cost of transportation are given in the following table. Find an initial basic feasible

solution using a. North West Corner Method b. Least Cost Method c. Vogel

approximation Method (VAM) d. Find optimal solution using stepping stone algorithm

(20 Marks)

Company Warehouses

A B C Supply

W 10 8 9 15

X 5 2 3 20

Y 6 7 4 30

Z 7 6 9 35

Requirement 25 26 49 100

  1. you are to prepare a work breakdown structure, draw the network diagram. A business is launching a new product. The launch will require a number of related activities as follows – hire a sales manager (5 weeks), require the sales manager to recruit salespeople (4 weeks), train the salespeople (7 weeks), select an advertising agency (2 weeks), plan an advertising campaign with the agency (4 weeks), conduct the advertising campaign (10 weeks), design the packaging of the product (4 weeks), set up packing operation (12 weeks), pack enough products for the launch stock (8 weeks), order the launch quantity of products from the manufacturer (13 weeks), select distributors for the product (9 weeks), take initial orders from the distributors (3 weeks), dispatch the initial orders to the distributors (2 weeks). 
A company produces two product A and B which sales at 5 and 10 shillings respectively. To produce them you required 3 and 2 labor hours of A and B respectively, 2 and 5 machine hours of A and B respectively. 5 litres of blue paint and 4 green paints for B and 3 litre green paint A. In total the company has 400 litres of blue paint, 400 litres of green paint, 400 machine hours and 400 labor hours.

Work out the optimization function and use your answers to match the questions that follow ( Assume x and y represent the number of product A and B produced respectively)
1.two machines (I and II) produce two grades of tires, A and B.in one hour of operation, machine i produces 20 unit of grade A and 10 units of grade B tires, while machine II produce 30 units of grade A and 40 units of grade B tires. the machines are required to meet a production schedule of at least 1400 units of grade A and 1200 units of grade B tires. the cost of operating machine I is $50 per hour and the cost of operating machine II is $80 per hour. based on the given information:-
A. formulate the linear programming model
B. determine the optimal solution if the objective is to minimize the cost of operating the machines using graphic method to solve the problem.
1. As part of a campaign to promote its annual clearance sale, Fanvis Supermarket decided to buy television advertising time on SoftCity TV. Fanvis' television advertising budget is GH¢10,000. Morning time costs GH¢300 per minute, afternoon time costs GH¢100 per minute, and evening (prime) time costs GH¢1,200 per minute. Because of previous commitments, SoftCity cannot offer Fanvis more than 6 minutes of prime time or more than a total of 25 minutes of advertising time over the two weeks in which the commercials are to be run. SoftCity estimates that morning commercials are seen by 200,000 people, afternoon commercials are seen by 100,000 people and evening commercials are seen by 600,000 people.
i) Formulate a Linear Programming Model for the given problem.
ii) Using simplex method, write the initial tableau
iii) How much morning, afternoon, and evening advertising time should Fanvis buy to maximize exposure of its commercials? Hence, state the maximum total people to be exposed.
Two players A and B are involved in a game. Each player has three different strategies. The pay-off table is given below
[ 5 -7 -17
A 4 6 -15 (in matrix)
9 10 -13]
Find the saddle point and value of the game.
Linear program assignments A farmer owns 5 hectares of land and thinks of the type of crop to be planted with rice or corn. currently, the rainy season so that by planting rice can provide income of 20 tons / hectare and if planting corn can produce as much as 15 tons / hectare. so that the results obtained are as expected, the farmer employs farm laborers with the assumption that if planting rice requires 30 hours-person / week and corn 10 hours-person / week. The available working time every week does not exceed 40 hours. at the same time the government issued a policy so that farmers produce at least 10 tons of corn for each harvest. The current price of rice is sold at Rp. 5000 / kg and the price of corn is sold at Rp. 4000 / kg. how is the formulation of this problem so that the farmer can optimize his land use?
Optimize{z=f(x,y)=6x^2-9x-3xy-7y+5y^2 }
using the step-by-step procedure.
Solve the following linear program using simplex algorithm: 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
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