Thread: How many items to produce to earn a profit?

A certain manufacturer produces items for which the production costs consists of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000?

Is my answer correct? My answer is 40,000. The way I got this was

130,000 +8 (x) + 150,000 = 15 (x)
280,000 + 8x = 15x
280,000 = 7 x
x= 40,000

Originally Posted by thecapaccino

A certain manufacturer produces items for which the production costs consists of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000?

Is my answer correct? My answer is 40,000. The way I got this was

130,000 +8 (x) + 150,000 = 15 (x)
280,000 + 8x = 15x
280,000 = 7 x
x= 40,000

i like your way, here's another (more explanatory) approach

let revenue be R(x)
let cost be C(x)
let profit be P(x)

the revenue is the money earned from selling x units, so R(x) = 15x

the cost is...well, the cost. we pay 130000 fixed cost no matter what, plus $8 per item, so C(x) = 8x + 130000

The profit is the money we make, that is the revenue minus the cost, so
P(x) = R(x) - C(x)
=> P(x) = 15x - 8x - 130000
=> P(x) = 7x - 130000

we want a profit of 150000, that is, we want P(x) = 150000

=> P(x) = 150000 = 7x - 130000
=> 280000 = 7x
=> x = 40000

so you are correct

The cobwebs are coming off the brain.

Thanks!!! Actually, I like your way...more analytical....

Cheers

Originally Posted by thecapaccino

The cobwebs are coming off the brain.

Thanks!!! Actually, I like your way...more analytical....

Cheers

shorter methods are usually more elegant to me. but i usually use long methods when i'm on this site, since those methods explain the logic better