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1. Work out the problems in a neat sheet with all the required steps.
2. This Assignment paper contains 4 Questions.
Find the value(s) of x where the tangent line is horizontal to the graph of
2. The marketing research department for a company that manufactures and sells “note
book” computers established the following price demand and revenue functions:
p ( x ) = 2,000 − 60 x
R ( x ) = xp( x )
= x (2,000 − 60 x )
Price – demand function
C( x ) = 4000 + 500 x
where p(x ) is the whole sale price in dollars at which x thousand computers can
be sold and R(x) and C (x ) are in thousands of dollars. Both functions have
domain 1 x 25 .
Find the marginal cost.
Find the marginal Revenue at a production level of 15 and interpret the result.
Find the Profit function and marginal profit function.
Find the break-even points.
For what values of x will a loss occur? a profit occur?
3. The total sales S (in thousands of games) for a home video game t months after the
game is introduced are given by S (t ) = 2 t + 10 . Find S (15) and S (15) and use
these results to estimate the total sales after 16 months.
4. The total cost (in dollars) of producing x bicycles is C (x ) = 5000 + 40 x + 0.05x .
exact cost of 101st bicycle
Find the marginal cost at a production level of 100 bicycles and interpret the
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price demand function
marginal profit function
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