The deal your assistant signs calls for the sale of a minimum of 260 chairs and up to 410 chairs. The price will be $88 per chair if only 260 chairs are bought, but will be discounted by $0.2 per chair (on the entire order) for every chair ordered in addition to the minimum. Answer the questions below, rounding your answers to the nearest whole dollar.
a) What is the largest revenue you can make under this deal?
revenue = $
b) What is the least revenue you can make under this deal?
revenue = $
a) To find the largest revenue, we need to consider the scenario where the maximum number of chairs (410 chairs) are bought.
Revenue = Number of chairs * Price per chair
Maximum revenue = 410 * $88 = $<<410*88=36080>>36,080
Therefore, the largest revenue you can make under this deal is $36,080.
b) To find the least revenue, we need to consider the scenario where the minimum number of chairs (260 chairs) are bought.
Revenue = Number of chairs * Price per chair
Minimum revenue = 260 * $88 = $<<260*88=22880>>22,880
Therefore, the least revenue you can make under this deal is $22,880.
To determine the largest and least revenue under this deal, we need to consider the two extreme scenarios - where the minimum and maximum number of chairs are sold.
a) To find the largest revenue, we assume the maximum number of chairs (410) are sold at the discounted price.
Step 1: Calculate the additional chairs beyond the minimum requirement:
Additional Chairs = Maximum Chairs - Minimum Chairs
Additional Chairs = 410 - 260
Additional Chairs = 150
Step 2: Calculate the discount per chair:
Discount per Chair = $0.2
Step 3: Calculate the total discount:
Total Discount = Additional Chairs * Discount per Chair
Total Discount = 150 * $0.2
Total Discount = $30
Step 4: Calculate the revenue:
Revenue = (Minimum Chairs * Price per Chair) - Total Discount
Revenue = (260 * $88) - $30
Therefore, the largest revenue under this deal is $22,850.
b) To find the least revenue, we assume only the minimum number of chairs (260) are sold at the full price.
Step 1: Calculate the revenue:
Revenue = Minimum Chairs * Price per Chair
Revenue = 260 * $88
Therefore, the least revenue under this deal is $22,880.
So, the largest revenue you can make under this deal is $22,850, and the least revenue you can make is $22,880.
the domain is 260 <= x <= 410
the price per chair is 88.00 - 0.02(x-260)
revenue is price * quantity, so
R(x) = x(88.00-.02(x-260))
= 93.2x - .02x^2
For maximum revenue, just find the vertex of the parabola.
For minimum, figure the revenue at the two ends of the domain, and choose the least.