# Mathematics problem-IIT level

#### JCB_india

##### New member
A company blends two materials: A and B to produce two types of fertilizers. Fertilizer 1
must be at least 45% of A and sells for $65 per kilo gram. Fertilizer 2 must be at least 70% of B and sells for$48 per kilogram. The price of martial A is $10 per 100 kilo grams and the price of martial B is$14 per 100 kilo grams if they purchased over 10,000 kilo
gram the price will be reduced by 10%. Total budget of the company to spend on raw
martial is $1600. a) Write the linear optimization model for the company to make the best decision. b) Solve the model and present the results and interpret them. c) Rewrite the model if 10% discount only apply to the amount purchased over 10000 kilo grams (For example if the company purchases 1001 kg of A, the total price is 1000*10+1*9). #### Subhotosh Khan ##### Super Moderator Staff member A company blends two materials: A and B to produce two types of fertilizers. Fertilizer 1 must be at least 45% of A and sells for$65 per kilo gram. Fertilizer 2 must be at least
70% of B and sells for $48 per kilogram. The price of martial A is$10 per 100 kilo grams
and the price of martial B is $14 per 100 kilo grams if they purchased over 10,000 kilo gram the price will be reduced by 10%. Total budget of the company to spend on raw martial is$1600.
a) Write the linear optimization model for the company to make the best decision.
b) Solve the model and present the results and interpret them.
c) Rewrite the model if 10% discount only apply to the amount purchased over 10000 kilo
grams (For example if the company purchases 1001 kg of A, the total price is
1000*10+1*9).
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