# Question: a the total cost function is given by cx ...

###### Question details

a. The total cost function is given by C(x) = −2x^{3} +
70x^{2}− 315x + 450,where x is the number of units produced
and sold. Show that x = 30 units of output is the only
real output level at which total cost will be zero.

b. At the end of an advertising campaign,monthly sales of cell
phones declined according to the equation S(t) =
150(4−^{0.03t}) thousand
dollars, where t is the number of months

after the campaign ended.

i. What will be the level of sales at the end of
the campaign?

ii. What will be the level of sales 3 years after the
end of the campaign

iii. How many months will it take on average for monthly sales to reach $80,000?