Question about linear functions with several variables

• Sep 12th 2011, 02:58 PM
m58
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

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!
• Sep 12th 2011, 03:06 PM
pickslides
Re: Question about linear functions with several variables
Quote:

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?
• Sep 12th 2011, 03:22 PM
m58
Re: Question about linear functions with several variables
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.
• Sep 12th 2011, 04:01 PM
m58
Re: Question about linear functions with several variables
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
• Sep 12th 2011, 05:26 PM
pickslides
Re: Question about linear functions with several variables
Quote:

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!