c, write an equation for the Profit function ptx) K-9A-30000 d) How many i n mus

Question

c, write an equation for the Profit function ptx) K-9A-30000 d) How many i n must be sold to b 20000 nord er to breakeven-=30000 x- e) Find the profr or seiniz2 tles of the ssunscreen P(80):0000)-30000. 54000-300 . Selling 6000 ottes 4) The unit cost, in dollars, to produce x tubs of ice cream is $2 and the fixed cost is $12814. The rew function, in dollars, is R(x) =-2x2+386x a) Find the profit function. P(x) b) What is the profit (or loss) when 25 tubs of ice-cream are sold? c) At what quantity is the smallest break-even point?

Explanation / Answer

Find cost function as

C(x)=2x+12814

a)

Find profit as

P(x)=R(x)-C(x)

=(-2x²+386x)-(2x+12814)

= -2x²+384x-12814

b)

Substitute x=25

P(25)= -2*25²+384*25-12814

= -4464

Hence loss of $4464

c)

At break even

P(x)=0

-2x²+384x-12814=0

-2(x-149)(x-43)=0

x=43, 149

Hence smallest quanity is 43.

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