The owner of a farm has 30 regular workers who each bring the farm a profit of $200 per day. For each additional worker hired, this profit decreases by $2.75 per day. How many additional workers should the owner hire to maximize profits?
I don't know where to start.
Answers
Answer:
21 Additional Workers should be hired
Step-by-step explanation:
The owner of a farm has 30 regular workers who each bring the farm a profit of $200 per day
=> Profit = 30 * 200 = $ 6000
For each additional worker hired, this profit decreases by $2.75 per day
Let say x workers are added
the Profit = (30 + x) ( 200 - 2.75x)
P = (30 + x) ( 200 - 2.75x)
=> P = 6000 + 117.5x - 2.75x²
dP/dx = 117.5 - 5.5x
put dP/dx = 0 => x = 21.36 ( x should be in integer)
so x = 21 or 22 ( Will check both cases)
d²P/dx² = - 5.5 ( -ve , hence value of x will give maximum profit)
Profit when x = 21
(30 + 21)(200 - 21*2.75)
= 51 * 142.25
= 7,254.75 $
Profit when x = 22
(30 + 22)(200 - 22*2.75)
= 52 * 139.5
= 7,254 $
7,254.75 > 7254
Hence x = 21 will give Maximize profit , after that profit will start decreasing
21 Additional Workers should be hired