Question 858266: The cost of producing x number of products is given by C(x)=115x + 51,471. Income from the sale of these products is given by R(x)=502x.
a) Find the cost to produce 250 products
b) Find the average cost if 400 products are produced
c) Find the profit function, P(x)
d) Will a profit or loss occur if 100 products are made or sold?
e) Find the break-even quantity of products
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! The cost of producing x number of products is given by C(x)=115x + 51,471. Income from the sale of these products is given by R(x)=502x.
a) Find the cost to produce 250 products
C(x)=115x + 51,471
C(x)=115*250 + 51,471
= $80,221. 00
b) Find the average cost if 400 products are produced
=115*400 + 51,471
=97471
Mean = 97471/400 =$243.68
c) Find the profit function, P(x)
P(x) = R(x) - c(x)
P(x)=502x-115x - 51,471
=387x -51,471
d) Will a profit or loss occur if 100 products are made or sold?
P(x) = R(x) - c(x)
=387x -51,471
P(100) = 38700-51,471
=-12771
The negative sign indicates that it will be a loss
=
e) Find the break-even quantity of products
For break even R(x) = C(x)
502x=115x + 51,471
387x= 51471
x= 51471/387
x= 133 the break even quantity
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