You run a small furniture business. You sign a deal with a customer to deliver up to 500 chairs, the exact number to be determined by the customer later. The price will be $120 per chair up to 400 chairs, and above 400 the price will be reduced by $0.25 per chair (on the whole order) for every additional chair over 400 ordered. What is the largest revenue your company can make under this deal?

I've found the minimum to be zero for this problem because they could sell no chairs at all and from what I can deduct from the problem the maximum they can make should be selling 400 chairs at $120 each which would be $48000 but my online turn in keeps telling me that's wrong and I don't understand why that is, please help.

120 times 400 + 119.75 times 100

I think they may be including the extra 100 chairs.

product of 7 and x decreased by x

To find the largest revenue your company can make under this deal, you need to consider the different scenarios based on the number of chairs ordered by the customer. Let's break it down step by step.

1. If the customer orders less than or equal to 400 chairs:
- In this case, the price per chair is $120.
- Let's assume the customer orders 'x' chairs, where x <= 400.
- The revenue for this scenario can be calculated as: Revenue = Price per chair * Number of chairs ordered.
- So, the revenue for this scenario is: Revenue = $120 * x.

2. If the customer orders more than 400 chairs:
- In this case, the price per chair is reduced by $0.25 for every additional chair over 400.
- Let's assume the customer orders 'y' chairs, where y > 400.
- Now, to calculate the revenue, we need to consider two parts:
a. Revenue for the first 400 chairs: $120 * 400.
b. Revenue for the additional chairs (above 400): Price per chair * Number of additional chairs.
- The price per chair for the additional chairs is reduced by $0.25, so it becomes $120 - $0.25.
- Therefore, the revenue for the additional chairs is: Revenue = (Price per chair for additional chairs) * Number of additional chairs.
- Simplifying the equation, the revenue is: Revenue = ($120 - $0.25) * (y - 400).

Now, to find the largest revenue your company can make, you need to compare the revenues from both scenarios.

- If the customer orders less than or equal to 400 chairs, the revenue is $120 * x.
- If the customer orders more than 400 chairs, the revenue is ($120 - $0.25) * (y - 400).

Since the problem doesn't provide any information about 'x' or 'y', you need to find the maximum value for the revenues in both scenarios.

So, the largest revenue will depend on 'x' and 'y'. Without additional information, it is not possible to determine the exact largest revenue your company can make under this deal.