SOLUTION: The table shows the daily production level and profit for a business. Use the quadratic function {{{ y=ax^2+bx+c }}} to determine the number of units that should be produced eac

Question 1137649: The table shows the daily production level and profit for a business. Use the quadratic function
to determine the number of units that should be produced each day for maximum profit. What is the maximum daily profit?
______________________________________________________________
x (Number of Units Produced Daily) | 30 | 50 | 100
______________________________________________________________
y (Daily Profit) | $5800 | $7320 | $4120

Each day [??] units should be produced to have a maximum daily profit of $[????].
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

The table shows the daily production level and profit for a business. Use the quadratic function
to determine the number of units that should be produced each day for maximum profit. What is the maximum daily profit?
______________________________________________________________
(Number of Units Produced Daily) | | |
______________________________________________________________
(Daily Profit) | $ | $ | $

........plug in and

..........solve for
.......eq.1

........plug in and

..........solve for
.......eq.2

........plug in and

..........solve for
.......eq.3

from eq.1 and eq.2 we have
......solve for

...........eq.1a

from eq.2 and eq.3 we have
.....solve for

..........eq2a

from eq.1a and eq.2a we have

.....solve for

go to ...........eq.1a, substitute

go to .......eq.3, substitute and

so, your function is:
max is at vertex, so write your function in vertex form where and are coordinates of the vertex

....using completing square we have

....

=> and

Each day units should be produced to have a maximum daily profit of $.

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