The manager of a small furniture manufacturing company has agreed to deliver an
ID: 2632110 • Letter: T
Question
The manager of a small furniture manufacturing company has agreed to deliver an order of up to 600 chairs to a customer. If the size of the order is 400 chairs or less, the price per chair will be $60. If more than 400 chairs are ordered, then the price per chair will be discounted by $.20 for each chair over 400 ordered (the discounted price applies to the entire order). Let R(x) denote the revenue from an order of x chairs.
A.) Calculate R(320) and R'(320). Label each appropriately.
B.) Calculate R(450) and R'(450). Label each appropriately.
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Explanation / Answer
The manager of a small furniture manufacturing company has agreed to deliver an order of up to 600 chairs to a customer. If the size of the order is 400 chairs or less, the price per chair will be $60. If more than 400 chairs are ordered, then the price per chair will be discounted by $.20 for each chair over 400 ordered (the discounted price applies to the entire order). Let R(x) denote the revenue from an order of x chairs.
A.) Calculate R(320) and R'(320). Label each appropriately.
Since this is less than 400, we know the price of each chair is $60
Let x = number of chairs
R(x) = 60x
R(320) = (60)(320) = $19200
R'(x) = 60
R'(320) = $60
B.) Calculate R(450) and R'(450). Label each appropriately.
Since the number of chairs is more than 400, we know that the price will be $60 - $0.20 for each chair over 400.
The price can be represented mathematically as:
p = $60 - $0.20(x-400)
p = $140 - $0.20x
Since Revenue = price x number sold
R(x) = x(140 - 0.20x)
R(x) = 140x - 0.20x2
R(450) = (140)(450) - 0.20(450)2
R(450) = $22,500
R(x) = 140x - 0.20x2
R'(x) = 140 - 0.40x
R'(450) = $140 - (0.40)(450) = -$40
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