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Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at least 21% of metal A, no more than 12% of metal B, no more than 70% of metal C, and between 30% and 65% of metal D. The proportion of the four metals in each of the six ores and the level of impurities in each ore are provided in the following table: Metal % Ore          A            B             C              D             Impurities (%) Cost/Ton 1              19          15            12            14                    40             $27 2              43         10            25             7                     15             $25 3              17           0             0             53                    30            $32 4              20         12             0             18                    50            $22 5               0          24           10             31                    35            $20 6             12          18             16           25                    29            $24 When the metals are processed and refined, the impurities are removed. The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy. a. Formulate algebraically the Linear Programming (LP) model for the above problem.

Question

Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at least 21% of metal A, no more than 12% of metal B, no more than 70% of metal C, and between 30% and 65% of metal D. The proportion of the four metals in each of the six ores and the level of impurities in each ore are provided in the following table: 

Metal %
Ore          A            B             C              D             Impurities (%) Cost/Ton 
1              19          15            12            14                    40             $27 
2              43         10            25             7                     15             $25 
3              17           0             0             53                    30            $32 
4              20         12             0             18                    50            $22 
5               0          24           10             31                    35            $20 
6             12          18             16           25                    29            $24 

When the metals are processed and refined, the impurities are removed. 

The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy. 



a. Formulate algebraically the Linear Programming (LP) model for the above problem. 

check_circleAnswer
Step 1

Linear programming:

It is a mathematical modelling method in which a linear function is maximized or minimized according to different constraints present in a scenario. It is being used as an important method in guiding and making quantitative decisions.

Step 2

Formulation:

 

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