Question

Original answer please don't copy and paste from other answers

Metallica Enterprise Ltd. can produce Copper, Steel and Aluminum at its factories at two cities. The factory in New Jersey can produce 6 tons of Copper, 2 tons of Steel, and 4 tons of Aluminum per day. The factory in San Francisco can produce 2 tons of Copper, 2 tons of Steel, and 10 tons of Aluminum per day. The rent of factory at New Jersey is $6000 per day and rent of factory at San Francisco is $7000 per day. The company has to export at least 12 tons of Copper, 8 tons of Steel and 5 tons of Aluminum to one of its customers. How many days should Metallica Enterprise Ltd. operate the factories in New Jersey and San Francisco so that it can meet the customer requirement at lowest rent.

1. a) Formulate a linear programming model for this problem. 5 marks

2. b) Solve the linear programming model formulated in (a) graphically and using computer and find

   the optimal solution. Match your answers. 10+10 marks

3. c) Write the sensitivity ranges for the objective function coefficients and the constraint quantity

   values using computer. 5 marks

4. d) Determine the extra Copper, Steel, and Aluminum the company produces at the optimal solution.

   5 marks

5. e) Further to part b), if the rent of factory at New Jersey increased to $7,500 per day, how will the

   optimal solution change? 5 marks

6. f) Further to part b), if the customer requests to increase the supply of copper to 20 tons per day,

   what will be the effect on optimal solution.

Answer 1

Let the factory in New Jersey is operated for x days.

Let the factory in San Francisco is operated for y days.

Total production of Copper in both factories = 6x + 2y

Total production of Steel in both factories = 2x+2y

Total production of Aluminium = 4x+10y

Total rent = 6000x +7000y

The linear equations are-

6x+2y>=12

2x+2y>=8

4x+10y>=5

Required to find the Lowest value for 6000x+7000y

subject to x>0, y>0