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12-73.
  1. Acme office furniture is selling computer chairs for $145 each, and they are looking for ways to increase sales revenue. They have found that companies have bought an average of 64 chairs per order, so they decide to offer a lower price on larger orders. They are considering the following plan: the cost will be $145 per chair for 80 or fewer chairs, but for each chair over 80, they will give a discount of 50¢ per chair on the entire order. What is the maximum amount that any customer would have to pay for an order of chairs under this plan? Homework Help ✎

    1. $17,112.50

    2. $13,912.50

    3. $21,312.50

    4. $145.00

    5. There is no maximum amount.

Only consider orders ≥ 80 chairs.

The cost of the chairs before the discount is 145x for x chairs.

The discount for 81 chairs is 0.50(1)(81).
The discount on 82 chairs is 0.50(2)(82).
The discount on 83 chairs is 0.50(3)(83).
...

The discount amount is 0.50(x – 80)x.

Write an equation for the total cost, including the discount.
Then maximize the equation.
Remember, x = # of chairs and the problem asks for the cost.