1 ahmed has started his own company masood shirts which...

Ahmed has started his own company, Masood Shirts, which manufactures imprinted shirts for special occasions. Since he has just begun this operation, he rents the equipment from a local printing shop when necessary. The cost of using the equipment is BD 350. The materials used in one shirt cost BD 8, and Ahmed can sell these for BD 15 each. Requirements: a) Identify the parameters of the problem b) Create the mathematical model that represents the problem c) If Ahmed sells 20 shirts, what would be the profit? d) How many shirts must Ahmed sell to break even?

Transcript

00:01 All right, friends, let's take a look at this problem together.

00:02 So in this particular situation, we have a t -shirt seller, somebody who is selling t -shirts.

00:09 So let's write that down.

00:10 We've got selling t -shirts.

00:13 Now, this particular person, when they're selling t -shirts, is going to rent the equipment.

00:23 We're renting the equipment for $350.

00:27 So $350 is how much we are renting the equipment for.

00:30 And what we understand is that the materials for each shirt are going to cost $8.

00:41 And we can sell the shirts for $15.

00:47 So what that means is that per shirt we're making a profit of $7.

00:53 And i just subtracted what we're selling it for the materials of the shirt.

00:58 So this person is making $7 for each shirt.

01:01 Now, a couple of things here.

01:02 We need to set up an equation that represents this situation.

01:06 But let's talk about profit first.

01:08 So profit is the amount of money minus the materials.

01:14 But in this case, we also have to rent the equipment, which is also another type of material.

01:19 So profit is going to equal, or well, i guess the amount of money that we make.

01:27 Let me erase this real quick.

01:30 There we go.

01:32 Okay.

01:32 So the money that we make in our pocket that goes to the bank is equal to our amount of total profit that we make from selling t -shirts profit minus expenses and um so this is going to be uh well actually let's let's make this even more clear instead of saying profit here let's do this we're going to put our profit here because profit is really what you put in the bank this is really what you put in the bank this is is the money that you're putting in the bank.

02:09 And this is how much our net earnings are.

02:15 And this means this is the amount of money that we have made from selling all of our t -shirts forgetting how many expenses or material that we have purchased.

02:26 So if we think about this, let's break it down here.

02:29 I'm going to change colors here so that we can write this out.

02:32 All right, so profit.

02:33 This is the amount of money that you're going to make.

02:35 Net earning.

02:37 We know that by selling each t -shirt, we are making $7.

02:41 So we're going to say $7 times x amount of t -shirts is equal to.

02:46 And then my expenses.

02:48 So the expenses that we have going on here are going to be the materials for our t -shirts as well as the rental equipment.

02:57 Now, we've already taken into account the net earnings here.

03:00 So we are saying that we're selling t -shirts for $15.

03:03 The materials for each t -shirt were $8.