Operations Research Answers

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:-

Required:-

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.

Two players A and B are involved in a game. Each player has three different strategies. The pay-off table is given below

B

[ 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

(a) Newbury Fastenings produce two kinds of specialized machine components, S10X and S10Y for which demand exceeds capacity. The production costs for the two products are given in the table below:


S10X S10Y

per component per component

Materials in Kg

(at £8 per Kg) 3 2


Labour in hours

(at £7 per hour) 2 3


Other Variable Costs (£) 6 5



The selling prices of the two products are £79 per unit and £67 per unit respectively. The production manager has stated at the monthly review meeting that there will only be 4,500 kg of material and 4,000 labour hours available next month. The company works on Just-in-Time manufacturing so holds no stocks and it wishes to maximize its profit.

How should the manufacturer arrange the production for next month in order to maximize contribution to profit? Determine the optimum level of contribution to profit.

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

A company manufactures two kinds of ice-cream. The vanilla ice-cream sells for $2.50 each while the chocolate flavour ice-cream sells for $4.50 cents each. It costs the company 1 labour hour to make the vanilla flavour ice-cream and 2 labour hours to make the chocolate flavour ice-cream. The company has a total of 300 labour hours available. It costs the company 3 machine hours for the vanilla ice-cream and 2 machine hours for the chocolate ice-cream. The company has a total of 480 machine hours available. How much of each type of ice-cream should the company produce to maximise revenue? What is the maximum revenue?

A company manufactures two kinds of ice-cream. The vanilla ice-cream sells for $2.50 each while the chocolate flavour ice-cream sells for $4.50 cents each. It costs the company 1 labour hour to make the vanilla flavour ice-cream and 2 labour hours to make the chocolate flavour ice-cream. The company has a total of 300 labour hours available. It costs the company 3 machine hours for the vanilla ice-cream and 2 machine hours for the chocolate ice-cream. The company has a total of 480 machine hours available. How much of each type of ice-cream should the company produce to maximise revenue? What is the maximum revenue?