Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars)
for a run of x pairs of cleats is C(x) = 3100 + 9x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing sells the cleats at $100 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?
1 answer:
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
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
You might be interested in
Answer: One tail test.
Step-by-step explanation:
Given : A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3.
Also, The set of hypothesis to conduct a test :-
The kind of test need to perform is dependent upon the alternative hypothesis.
Since, the alternative hypothesis is one tailed (right-tailed), so the test is one tail test.