Show and explain work Fantastic Flags Inc finds that the cos

Show and explain work.

Fantastic Flags, Inc. finds that the cost to make x flags is1244whie the revenue produced from them is (C and R are in dollars). What is the smallest whole number of flags, x, that must be sold for the company to show a profit? Roberto invested some money at 7%, and then invested $300 more than twice this amount at 9%. His total annual income from the two investments was $3770. How much did he invest at 9%?

Solution

1) C(x) = 22x +12442

R(x) = 30x

Profit = R(x) - C(x) >0

30x -22x -12422 >0

8x> 12422

x > 1552.75

which means he should sell atleast 1553 flags to have profit

2) Let assume he invested $x at 7%

So, interest = x*0.07*1 = 0.07x

2nd amt : 3000+2x at 9%

So, interest = 0.09(3000+2x)

Total annual income = 270 +0.18x

Total annual income = $3770

3770 = 0.07x + 270 +0.18x

3500 = 0.25x

x = $ 14000

Amt at 9% = 2*14000 +3000 = $31000