SOLUTION: A manufacturer of custom drinking mugs has the capacity to produce 1,800 mugs per day. It has a fixed daily cost of $1,000 plus a variable cost of $1.50 per mug. a)How many mugs w

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Question 168227: A manufacturer of custom drinking mugs has the capacity to produce 1,800 mugs per day. It has a fixed daily cost of $1,000 plus a variable cost of $1.50 per mug.
a)How many mugs were created in a batch that had a total daily cost of $2,800?
b)The total cost of mugs can also be calculated by multiplying the average cost per mug by the number of mugs produced. If the company needs to reach an average cost of $2.00 per mug, how many mugs must it produce per day?
Answer by hobbitt(2) (Show Source):
You can put this solution on YOUR website!
Daily cost is $1,000 + $1.50x
ie amount to run factory for the day is $1,000 (fixed cost) and x is the number of cups made costing $$1.50 in materials
If Total = $2,800
then $2,800 = $1,000 + $1.50x
subtract $1,000 to get the x term alone to give
$2,800 - $1,000 = $1.50x
$1,800 = $1.50x
now divide both sides by $1.50 to get x on its own
$1,800/$1.50 = x
so x = # cups made to produce $2,800 daily cost is 1200 cups
Not sure what the 2nd part is asking
but if they want the mugs to be $2.00 each then
If Total = $2,800
then $2,800 = $1,000 + $2.00x
subtract $1,000 to get the x term alone to give
$2,800 - $1,000 = $2.00x
$1,800 = $2.00x
now divide both sides by $2.00 to get x on its own
$1,800/$2.00 = x
so x = # cups made to produce $2,800 daily cost is 900 cups