Instructions 1 The manager of an oil refinery must decide on the optimal mix of two possible blending processes of which theinput and output per production run are given as follows Process Units Input Crude A Crude B Output Gasoline X Gasoline Y 1 5 3 5 8 2 4 5 4 4 The maximum amount available of crude A and B are 200 units and 150 units respectively Market requirements show that at least 100 units of gasoline X and 80 units of gasoline Y must be produced The profit per production run from process 1 and process 2 are Rs 300 and Rs 400 respectively Formulate this problem as a linear programming model 2 A city police department has the following minimal daily requirement for policeman Note, you are to consider period 1 as following immediately after period 6 Each policeman works eight consecutive hours Let X denote the number of men starting work in period t everyday The police department seeks a daily manpower schedule that employs the least number of policemen, provided that each of the above requirements is met Formulate linear programming model to find an optimal schedule Time of Day Period Minimal number of police required during a period 2 6 1 20 6 10 2 50 10 14 3 80 14 18 4 100 18 22 5 40 22 2 6 30 3 A car dealer selects his cars for sale very carefully so as to ensure the optimization of his profits He deals in 4 types of cars A, B, F and G The purchase value of the cars range at Rs 60,000, 150,000, 55,000 and 220,000 and the sales value is fixed at Rs 80,000, 175,000, 75,000 and 250,000 respectively The probability of sale are 0 8, 0 9, 0 6 and 0 50 respectively during a period of six months In order to invest Rs 20,00,000 in his deals, he wishes to maintain the rates of purchase of cars as 3 1 2 4 Work out how and how much he should buy Formulate this problem as LP model 4 Use graphical method to solve the following LP problems Max Z 3x 1 4x 2 Subject to 2x 1 x 2 10 x 1 3x 2 12 x 1 x 2 6 x 1, x 2 0 Problem 1 Answer Objective Z Constraints Input Crude A Input Crude B Output Gasoline X Output Gasoline Y Non Negative Constraints Problem 2 Answer Objective Z Constraints Non Negative Constraints Problem 3 Answer Objective Z Constraints Non Negative Constraints Problem 4 Answer Insert a chart

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Instructions 1. The manager of an oil refinery must decide on the optimal mix of two possible blending processes of which theinput and output per

Instructions

1. The manager of an oil refinery must decide on the optimal mix of two possible blending processes of which theinput and output per production run are given as follows:

Process Units

Input

Crude A

Crude B

Output

Gasoline X

Gasoline Y

The maximum amount available of crude A and B are 200 units and 150 units respectively. Market requirements show that at least 100 units of gasoline X and 80 units of gasoline Y must be produced. The profit per production run from process 1 and process 2 are Rs. 300 and Rs. 400 respectively. Formulate this problem as a linear programming model.

2. A city police department has the following minimal daily requirement for policeman. Note, you are to consider period 1 as following immediately after period 6. Each policeman works eight consecutive hours. Let X denote the number of men starting work in period t everyday. The police department seeks a daily manpower schedule that employs the least number of policemen, provided that each of the above requirements is met. Formulate linear programming model to find an optimal schedule.

Time of Day	Period	Minimal number of police required during a period
2 - 6	1	20
6 - 10	2	50
10 - 14	3	80
14 - 18	4	100
18 - 22	5	40
22 - 2	6	30

3. A car dealer selects his cars for sale very carefully so as to ensure the optimization of his profits. He deals in 4 types of cars A, B, F and G. The purchase value of the cars range at Rs. 60,000, 150,000, 55,000 and 220,000 and the sales value is fixed at Rs. 80,000, 175,000, 75,000 and 250,000 respectively. The probability of sale are 0.8, 0.9, 0.6 and 0.50 respectively during a period of six months. In order to invest Rs. 20,00,000 in his deals, he wishes to maintain the rates of purchase of cars as 3 : 1 : 2 : 4. Work out how and how much he should buy. Formulate this problem as LP model.

4. Use graphical method to solve the following LP problems

Max. Z = 3x₁ + 4x₂

Subject to

2x₁ + x₂ ? 10

x₁ + 3x₂ ? 12

x₁ + x₂ ? 6

x_1, x₂ ? 0

Problem 1 Answer: Objective: Z = Constraints: Input Crude A: Input Crude B: Output Gasoline X: Output Gasoline Y: Non-Negative Constraints: Problem 2 Answer Objective: Z = Constraints: Non-Negative Constraints: Problem 3 Answer Objective: Z = Constraints: Non-Negative Constraints: Problem 4 Answer Insert a chart