The level of diamond production sreeb chooses is Q = 185.
We know the profit function is POs = (370 - Q)Q. We need to find the level of diamond which is going to produce maximum profit. This is obtained when we differentiate POs with respect to Q and then equate it to zero.
So, dPOs/dQ = d(370 - Q)Q/dQ
= 370 - Q - Q
= 370 - 2Q
Let us equate this to zero.
So, dPOs/dQ = 0
⇒ 370 - 2Q = 0
Adding 2Q to both sides, we have
370 = 2Q
Dividing through by 2, we have
Q = 370/2
Q = 185
The level of diamond production Sreeb chooses is Q = 185.
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