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
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Answer:
(a) $248.285
(b) $249.441
(c) I will prefer to buy the television from online store.
Step-by-step explanation:
The manufacturing price of a television is $170.
(a) The online retailer charges a standard makeup of 27% and an additional 15% charge for shipping and tax.
Therefore the final price will be $
= $(170 × 1.27 × 1.15)
= $248.285
(b) Now, the superstore has makeup of 34% and then 9.5% charges for state tax.
So, the final price becomes $
= $(170 × 1.34 × 1.095)
= $249.441
(c) So, I will prefer to buy the television from the online store because the final price is less and also the shipping charges are included in the final price. (Answer)