Answer:
See the explanation below.
Explanation:
a. The number of widgets that will be sold
Let y represent the number of widgets that will be sold, and and we already have x as price of widget, we therefore have:
y - 1,000 = (-600/10) * (x - 389)
y - 1,000 = -60 * (x - 389)
y = 1,000 - [60 * (x - 389)
]
y = 1,000 - 60x + 23,340
y = 24,340 - 60x
b. The revenue generated by the sale of widgets
Let R represent Revenue, therefore we have:
R = xy
R = x(24,340 - 60x)
R = 24,340x - 60x²
c. The cost of producing just enough widgets to meet demand
Let C represent total cost, we therefore have:
C = 8,000 + 97.25y
C = 8,000 + 97.25(24,340 - 60x)
C = 8,000 + 2,367,065 - 5,835x
C = 2,375,065 - 5,835x
d. The proft from selling widgets
Let P represent profit, we therefore have:
P = R - C
P = 24,340x - 60x² - (2,375,065 - 5,835x)
P = 24,340x - 60x² - 2,375,065 + 5,835x
P = - 60x² + 30,175x - 2,375,065
e. Find the price that will maximize profits from the sale of widgets
Profit is optimum when dP/dx = 0
Therefore, we have
0 = - 120x + 30,175
120x = 30,175
x = 30,175/120 = $251.46
