Let's break down the information given and solve this step-by-step:

1. Minimum and Maximum Order:

   • Minimum chairs: 270
   • Maximum chairs: 440

2. Pricing:

   • If 270 chairs are bought, the price is $87 per chair.
   • For every chair above 270, there’s a discount of $0.25 per chair on the entire order.

3. Objective:

   • (a) Find the largest revenue the supplier can make.
   • (b) Find the least revenue the supplier can make.

Solution Approach

Let $x$ be the number of chairs ordered above the minimum 270. Therefore, the total chairs ordered is $270 + x$, where $0 \leq x \leq 170$ (since the maximum number of chairs is 440).

The price per chair, given the discount, becomes: $\text{Price per chair} = 87 - 0.25x$

The revenue, $R$, is then calculated by: $R = \text{Total Chairs} \times \text{Price per Chair} = (270 + x)(87 - 0.25x)$

Part (a): Maximum Revenue

To maximize the revenue, substitute $x = 0$ (for no additional chairs) and $x = 170$ (for the maximum chairs).

1. When $x = 0$: $R = 270 \times 87 = 23490$

2. When $x = 170$: $\text{Price per chair} = 87 - 0.25 \times 170 = 44.5$ $R = 440 \times 44.5 = 19580$

So, the maximum revenue is $23,490.

Part (b): Minimum Revenue

The minimum revenue happens at the maximum discount applied, which is when $x = 170$, resulting in a revenue of $19,580.

Answers

• (a) Largest revenue: $23,490
• (b) Least revenue: $19,580

Would you like further details or clarification on this solution?

Here are some related questions to consider:

1. How would the revenue change if the discount was $0.50 per additional chair instead?
2. What if the minimum order quantity was raised to 300 chairs?
3. How does the revenue formula change if a fixed discount is applied regardless of the number of chairs?
4. Could the revenue model be maximized with non-integer values of $x$?
5. What is the impact on revenue if the initial price per chair was different?

Tip: Always double-check units and ensure each step aligns with the conditions in the problem for accurate results.