Revenue: R(x) = 100x
Profit: P(x)= 3100 + 9x + 0.1x2 <span>(0 ≤ x ≤ 500)
</span><span>equalize the two equations
</span>100x=3100 + 9x + 0.1x2
0.1x2-91x+3100=0
<span>using graphic tools
x1=35.447----35
x2=874
the domain is </span>(0 ≤ x ≤ 500)
the value from which there are profits is 35 <span>pairs of cleats
</span>
Revenue: R(x) = 100x --------100*35=$3500
Profit: P(x)= 3100 + 9x + 0.1x2 -------3100+9*35+0.1*(35)2=$3537.5
Profit > Revenue up to the amount of 35 pairs of cleats
Explanation - 7.5 is greater than 7.05, therefore you would use the '>' symbol
Combine like terms:
-12 + 5a - a - 6a + 8a + 8 + 3a
5a - a = 4a
4a - 6a = -2a
-2a + 8a = 6a
6a + 3a = 9a
-12 + 8 = -4
Answer
If you cut it in half every two hours, the answer will be 10.9375 mg.