Express the total amount of money M she will receive for the shirts in terms of the number n of machines she decides to set up (assuming she sells all the shirt

Question

A manufacturer wishes to make tee-shirts for the band Dixie Chicks. They sell for $14 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money M she will receive for the shirts in terms of the number n of machines she decides to set up (assuming she sells all the shirts she makes).

 

Help please? I've tried solving and keep getting it wrong?

Answer 1

let x equal the number of days she sets up machines.  then the number of days of production would be 20-x.  For ease, if she only set up one machine and then started producing, she'd have 20-1 or 19 days of production

So the number of shirts she makes is going to be x(20-x)(200) since she will make 200 times every production day.

She gets 14$ for each shirt so the money she will get will be equal to the number of shirts times $14.

 

M = x(20-x)(200)($14)  That is an equation for M.  Its not simplified, but the question doesn't ask for a simplified expression.  I'll leave that to you, if you think its needed.