# math

A Company has introduced a new product whose annual demand will depend on price charged. The demand of the product is represented by the function q = 100,000 – 200p, (where p = price and q = quantity demanded annually). Studies indicate that total cost of producing q unit is represented by TC = 150,000 + 100q + 0.003 q2 quantity to be produced to maximize profit is:

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1. Tc=150000+100q+0.003q^2
Q=100000_200p
Max profit=?
At max profit ;MC=MR...eq (1)
Q=100000-200P
P=q_100000/_200
P=1/_200 q + 500
P=500-0.005q
TR=(500-0.005q)q
=500q-0.005q^2
MR=500-0.01q
From TC ; MC=100+0.006q
Putting MC and MR in eq (1)
500_0.01q=100+0.006q
500_100=0.006q+o.o1q
400=0.016q

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