Math

Basic Math Solutions

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The profit P (in thousands of dollars) for a company spending an amount s (in thousands of dollars) on advertising is shown
below.
P= -
1
-53
10
+ 1852 + 400
Exercise (a)
Find the amount of money the company should spend on advertising in order to yield a maximum profit.
Step 1
To find maximums or minimums, we differentiate P = - 133 + 1852 + 400 with respect to s, set it equal to
+
10
zero, and solve for s.
dP
3
S? + 36s = -
10
s(s
120
120)
ds
10
Step 2
We now find the values of s for which
dP
= 0.
ds
dP
3
-S(S - 120) = 0
10
ds
3
-S = OS=
10
S - 120 = 0 = S =
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