SOLUTION: A manufacture has a daily production cost of C=86,000-140x+0.075x^2, where C is the total cost in dollars and x is the number of units produced A. How many units should be produce

Algebra ->  Test -> SOLUTION: A manufacture has a daily production cost of C=86,000-140x+0.075x^2, where C is the total cost in dollars and x is the number of units produced A. How many units should be produce      Log On


   

Question 750951: A manufacture has a daily production cost of C=86,000-140x+0.075x^2, where C is the total cost in dollars and x is the number of units produced
A. How many units should be produced each day to yield the minimum cost?
B. what is the minimum cost?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A manufacture has a daily production cost of C=86,000-140x+0.075x^2, where C is the total cost in dollars and x is the number of units produced
A. How many units should be produced each day to yield the minimum cost?
C=86,000-140x+0.075x^2
C'(x) = -140 + 2*0.075x
-----
Solve: -140+0.15x = 0
0.15x = 140
x = 933.33 (# of units to produce minimum cost)
----
B. what is the minimum cost?
f(933.33) = $20,667
==========================
Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+C=86000-140x%2B.075x%5E2+
Rearrange the right side
+C+=+.075x%5E2+-+140x+%2B+86000+
The x- coordinate of the vertex is at
+x%5Bv%5D+=+-b%2F%282a%29+ where
+a+=+.075+
+b+=+-140+
+x%5Bv%5D+=+-%28-140%29+%2F+%28+2%2A.075%29+
+x%5Bv%5D+=+140+%2F+.15+
+x%5Bv%5D+=+933.333+
and
+C+=+.075%2A934%5E2+-+140%2A934+%2B+86000+
+C+=+.075%2A872356+-+130760+%2B+86000+
+C+=+65426.7+-+130760+%2B+86000+
+C+=+20666.7+
----------------
934 units should be produced each day to yield the minimum cost
The minimum cost is $20,666.70
hope I got it