Answer:
The largest revenue you can make is $22781 and you will make it if you sell 338 chairs.
The least revenue you can make is $20680 and you will make it in case you sell 440 chairs.
Step-by-step explanation:
Hi there!
The revenue is calculated by multiplying the number of chairs sold times the price of each chair. Let y be the revenue:
y = 250 · 85
If you sell more than 250 chairs, the price per chair will be discounted by $0.2 for every additional chair sold. So, if you sell x chairs more than 250, the discount per chair will be 0.2x. Then, the revenue, in this case, will be:
y = (250 + x) (85 - 0.2x)
Apply distributive property:
y = 21250 - 50x + 85x - 0.2x²
y = -0.2x² + 35x + 21250
The function is a negative parabola so that the largest revenue will be made at the vertex of the parabola. It is calculated using this formula:
x = -b/2a
Where:
a = -0.2
b = 35
Then:
x = -35/(2 · -0.2)
x = 87.5
Let´s round x to 88 because you can´t sell a half-chair.
Then , the maximum revenue will be:
y = -0.2x² + 35x + 21250
y = -0.2(88)² + 35(88) + 21250 = 22781
The largest revenue you can make is $22781 and you will make it if you sell 250 + 88 = 338 chairs.
Since the revenue function is a negative parabola the least revenue will be made at the extremes of the function (x = 0 and x = 440 -250 = 190). See the attached figure to notice this.
At x = 0
y = 21250
At x = 190
y = -0.2(190)² + 35(190) + 21250 = 20680
The least revenue you can make is $20680 and you will make it in case you sell 440 chairs.
