The rocket shoe manufacturing company has found that the cost of
manufacturing their line of slam dunk super sneakers decreases linearly from a
cost of $20 per pair for making 1000 pairs per day, at a rate of $1 per pair
for every additional thousand pairs made per day. At the 1000 pair per daymanufacturing rate, they can sell all they make for $90 per pair. For
every additional thousand pairs per day they try to sell they have to reduce
the price another $10 per pair for all of them. The company wants to know how
many pairs per day they can make and still get at least twice the manufacturing cost for them.
Plot these functions on a coordinate system
Write the equations for cost of manufacture and selling price
versus number of thousands of pairs of shoes manufactured. Use X for the
independent variable and you for the dependent variable in both cases.
What equations would you use to find the point where selling price
is exactly twice manufacturing cost? What will be the per pair manufacturing cost and selling
price at this point?
After the Rocket Shoe Company set up the above manufacture and
selling price schedules, they got a huge order from a famous nation-wide
department store chain offering to buy 9 thousand pairs of Slam-Dunk Super
Sneakers a day, at the stated usual price reduction of $1 per pair per
Decide from your equations if the Rocket Shoe Manufacturing
Company can make money on this deal.