# 10.6.3. Linear Programing and Optimization

A seafood restaurant sells two types of cooked fish; cod and eel. The restaurant sells NOT less than 40 fish every day. It doesn't consume more than 30 cods and NOT more than 45 eels. The price of a cod is LE and that of an eel is LE. If represents the amount of cod, represents the amount of eel, and represents the total price of fish, determine the relations that will help the restaurant manager in this situation.

• A, , , , ,
• B, , , , ,
• C, , , , ,
• D, , , , ,

### Example

A seafood restaurant sells two types of cooked fish; cod and eel. The restaurant sells NOT less than 40 fish every day. It doesn't consume more than 30 cods and NOT more than 45 eels. The price of a cod is LE and that of an eel is LE. If represents the amount of cod, represents the amount of eel, and represents the total price of fish, determine the relations that will help the restaurant manager in this situation.

### Solution

Suppose that is the number of cod, and is the number of eel.

It is impossible to consume a negative number of cod or eel, so both and must be greater than or equal to 0.

The words "not less than" indicate that the sum of and is greater than or equal to 40.

Also, the words "does not consume more than" indicate that is less than or equal to 30, and the words "not more than" indicate that is less than or equal to 45.

Since the price of a cod is LE, the total price of all cod is LE, and since the price of an eel is LE, the total price of all eel is LE.

Therefore, the total price, , of all the fish is LE.

This means that the relations that will help the restaurant manager in this situation are , , , , , .

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