Question

I have no clue what i’m doing

Answer 1

Explanation:

C(x)=16x+22736

R(x)=-2x²+524x

P(x)=R(x)-C(x)

=-2x²+524x-16x-22736

=-2x²+508-22736

when profit is zero then no gain or loss.

so -2x²+508x-22736=0

or x²-254x+11368=0

196+58=254

196×58=11368

x²-54x-196x+11368=0

x(x-54)-196(x-54)=0

(x-54)(x-196)=0

x=54,196

so x=54 is the smallest number of bins to break even.

Answer 2

c(x) = 16x + 22736

R(x) = -2x^2 + 524x

[ -2x^2 + 508x - 22736] = 0

Factored: f(x) = -2(x - 196)(x - 58)

58 to break even

Explanation:

Your cost is the amount it cost you to "make" stuff.

You have fixed and variable costs (cost of oven is fixed cost of flower and sugar is variable to make cupcakes)

your cost is c(x) = 16x + 22736

"your oven and building cost $22736 per month and you use $16 worth of sugar butter flour to make one cupcake ( it must be a huge one) ...

your revenue is the amount of money that "comes into your business"...

the amount of money in the cash register.... Note: this is only money IN you still have to pay for the building, sugar flour etc.

R(x) = -2x^2 + 524x

Note: the minus and the square basically say that the more you charge the less cupcakes you will sell...

Profit is the money in minus the money out

P - R - E [ -2x^2 + 524x ] - [16x + 22736]

the break even point is where the two functions are the same

in other words where C=R or R-C=0

[ -2x^2 + 524x ] = [16x + 22736]

[ -2x^2 + 508x - 22736] = 0

Factored: f(x) = -2(x - 196)(x - 58)