SOLUTION: A semiconductor manufacturer seeks to maximize its profits. Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip

Algebra ->  Functions -> SOLUTION: A semiconductor manufacturer seeks to maximize its profits. Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip      Log On


   

Question 169289: A semiconductor manufacturer seeks to maximize its profits. Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip. They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip. How much profit can they expect to earn if they produce 130,000 chips per week?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

So we need to know the cost%3F and selling%3F for 130,000 chips then.
Via the data given, we need to do INTERPOLATION to find the 2 unknowns.
.
First, we'll get the cost.
Let x=cost for 130,000 chips:
Based on Given--->system%28100000=40%2C125000=35%2C130000=x%29
By Interpolation: %28100000-125000%29%2F%28100000-130000%29=%2840-35%29%2F%2840-x%29
-25000%2F-30000=5%2F%2840-x%29, cross multiply
-1000000%2B25000x=-150000
25000x=1000000-150000=850000
cross%2825000%29x%2Fcross%2825000%29=cross%28850000%2934%2Fcross%2825000%29
x=$34.00/ea, cost
.
Next for the Selling price of 130,000 chips based on cost=$34.00/ea:
Based on Selling Price Given on other Quantities produced, let y=Selling.
By Interpolation --->system%2840=65%2C35=63%2Chighlight%2834%29=y%29
%2840-35%29%2F%2840-34%29=%2865-63%29%2F%2865-y%29
5%2F6=2%2F%2865-y%29, cross multiply
6%2A2=5%2865-y%29
12=325-5y
5y=325-12=313 ----> cross%285%29y%2Fcross%285%29=cross%28313%2962.60%2Fcross%285%29
y=$62.60/ea, Selling
.
For the Profit=Total+Selling-TotalCost, working eqn
TotalSelling=62.60%28130000%29=$8,138,000.00
TotalCost=34.00%28130000%29=$4,420,000.00
Then Via working eqn,
Profit=8138000-4420000
highlight%28Profit%29=$3,718,000.00 ---> Answer
Thank you,
Jojo