Answer:
<em>a) Since the income is more than the cost, she makes a profit.</em>
<em>b) To make profits, she must sell at least 17 necklaces</em>
Step-by-step explanation:
<u>Inequalities</u>
The costs of selling jewelry at a fair are $135 to rent a booth and $4 for each necklace. The cost function is:
C(n) = 135 + 4n
Where n is the number of necklaces she sells at the fair. She sells each necklace at $12 each, thus the income function is:
R(n) = 12n
a) If she sells n=17 necklaces, it will cost:
C(17) = 135 + 4*17 = 203
And the income is:
R(17) = 12*17= 204
Since the income is more than the cost, she makes a profit.
b) To make a profit R(n) > C(n), thus:
12n > 135 + 4n
Subtracting 4n:
8n > 135
n > 135/8
n > 16.875
Thus, to make profits, she must sell at least 17 necklaces
