Thread: Question about linear functions with several variables

Hi guys,

Just wanted to check over if I understood the following problems correctly:

1) Bill has a fixed cost of $215 per day to run his art business. Unit costs are .65 per paintbrush, which he then resells at 1.75 per brush. Express his daily profit in number of brushes sold.

So, is this correct?:
y = profit
x = each brush sold
.65 + 1.75 = 2.4
2.4x + 215 = y

2) Jake's publishing company sells books at 14.5 per unit. His publishing costs are 1400 per day, and he incurs unit costs of 3.85 each. Due to a new publishing process, his fixed costs increase to 1725 (this reduces the unit cost, making it 2.7 each). Express Jake's increase in profit as a linear function of sold books and publishing costs.

So I would do:

y = total units
x= each additional unit

14.5 + 3.85 = 18.35
1400 + 18.35x = y


14.5 + 2.7 = 17.2
1725 + 17.2x = y

(1725 + 17.2x) - (1400 + 18.35x) = 325 - 1.15x

Thanks!

Originally Posted by m58

Hi guys,

Just wanted to check over if I understood the following problems correctly:

1) Bill has a fixed cost of $215 per day to run his art business. Unit costs are .65 per paintbrush, which he then resells at 1.75 per brush. Express his daily profit in number of brushes sold.

Let x be the number of paintbrushes

Profit = Revenue - Cost

Profit = 1.75x - (215+0.65x) = ....

can you finish it?

Hmm... so it would be:

y = 1.75x - (215 + .65x) -> 1.1x - 215
So if he sold 5 brushes, his profit would be -209.5?

I should have put that the problem wants "the daily profit as a linear function of brushes sold". My bad.

Also, just figured out the second problem using your method, pickslides:

14.5x - (1400 + 3.85x) -> 10.65x - 1400
14.5x - (1725 - 8.7x) -> 11.8x - 1725

(11.8x - 1725) - (10.65x - 1400) = 1.15x - 325

Originally Posted by m58

y = 1.75x - (215 + .65x) -> 1.1x - 215
So if he sold 5 brushes, his profit would be -209.5?

Yep, nice work!