Thanks! The total cost C(q) of producing q goods is given by: C(q) = 0.01 - 0.6l

Question

Thanks!

The total cost C(q) of producing q goods is given by: C(q) = 0.01 - 0.6l + 12q What is the fixed cost? What is the maximum profit if each item is sold for 10 dollars? (Assume you sell everything you produce.) maximum profit = Suppose we fix production at 38 goods produced, and that they all sell when the price is 10 dollars each. Also suppose that for each 1 dollar increase in price, 1 fewer goods are sold (so if the price is 11 dollars, 37 of the 38 goods being produced are sold.) To maximize profit in this case, we should the price by dollars.

Explanation / Answer

fixed cost: cost at q=0

so here fixed cost=0

b)profit=revenue-cost of production

let number of items =q

then profit=q*10-0.01q^3+0.6*q^2-12*q=2*q-0.01*q^3+0.6*q^2

so derivative w.r.t q=0

==>2-0.02*q^2+1.2*q=0

so q=-1.62

or q=61.62

now as q should be an integer,

for q=61, profit=84.79

for q=62,profit=47.12

so maximum profit=84.79 dollars

Q3.let new price be 10+d.

cost of production=138.32

then profit=(38-d)*10-138.32

so derivative w.r.t. d=0

d=0

so there should not be any increment

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