Respuesta :
Answer:
a) Revenue obtained from selling x suits
R(x) = 180x - 0.5x²
b) Total Profit obtained from selling x suits
P(x) = -1.25x² + 180x - 4500
c) The number of units that should be produced and sold to maximize profits is 72 units.
d) Maximum Profit = $1,980
e) Price per suit that must be charged in order to maximize profit = $144
Step-by-step explanation:
Assume the price is in dollars.
Price per suit is given as
p = 180 − 0.5x
Cost of producing x suits
C(x) = 4500 + 0.75 x²
a) Revenue obtained from selling x suits
R(x) = px = x (180 − 0.5x) = 180x - 0.5x²
b) Total Profit = Revenue - Cost
= (180x - 0.5x²) - (4500 + 0.75x²)
= 180x - 1.25x² - 4500
P(x) = -1.25x² + 180x - 4500
c) in order to maximize profit, we find the maximum of the profit function.
At the maximum point, (dP/dx) = 0
P(x) = -1.25x² + 180x - 4500
(dP/dx) = -2.5x + 180 = 0
x = (180/2.5) = 72 units.
Therefore, the number of units that should be produced and sold to maximize profits is 72 units.
d) The maximum profit
To obtain this, we just slot in the number of units that should be produced and sold to maximize profits into the Profits function.
P(x) = -1.25x² + 180x - 4500
x = 72 units
P(x) = -1.25(72²) + 180(72) - 4500 = $1980
e) Price per suit that must be charged in order to maximize profit
Price per suit is given as
p = 180 − 0.5x
Slotting the number of units that should be produced and sold to maximize profits into this expression,
p = 180 - 0.5(72) = $144
Hope this Helps!!!
