Question

John boy and Mary Ellen own a food stand to make funnel cakes. they drive it to county fairs all over the state dyring the summer months. In their budget they have determined that they will have $1200.00 in fixed costs for the year. Each funnel cake that they sell uses dough, oil, and sugar which cost a total of $75 per 100 funnel cakes made, so the total cost can be calculated using formula C= 0.75x + 1200. For past three summers, they were able to sell their funnel cakes for $3.50 each, so the revenue can be calculated using the formula R=3.50x.(a). write the algebraic equation that indicates that the cost is equal to the revenue.(b). solve the equation from the previous question. explain the meaning of this solution.(c). write the algebraic inequality needed to indicate that the cost is less than the revenue.(d). solve the inequality from the previous equation. explain the meaning of its solution.

Answer 1

(a)0.75x+1200=3.50x

(b)
`x=436.36\approx 436, Break-Even \:Point`

(c)0.75x+1200<3.50x

(d)
`x>436.36\approx 436`

It means the store needs to sell more than 436 funnel cakes to make a profit

Explanation:

Given the Cost and revenue function of John boy and Mary Ellen's food stand below:

C= 0.75x+1200.

R=3.50x

(a)When Cost = Revenue

Then:

0.75x+1200=3.50x

(b)To solve the equality from part (a) above

0.75x+1200=3.50x

Collect like terms

1200=3.50x-0.75x

1200=2.75x

Divide both sides by 2.75

`x=436.36\approx 436`

When Cost equals revenue, it is the Break-Even Point. It means the food stand will have to sell 436 funnel cakes to break even.

(c) When Cost is Less than Revenue

`C(x)<R(x)\\0.75x + 1200<3.50x`

(d)Solving the inequality

C(x)<R(x)

0.75x + 1200<3.50x

Collect like terms

1200<3.50x-0.75x

1200<2.75x

Divide both sides by 2.75

`436.36<x`

`x>436.36\approx 436`

It means the store needs to sell more than 436 funnel cakes to make a profit.