the naturally made bath and body store pays $550 a month for rent and utilities. the average cost for its…

the naturally made bath and body store pays $550 a month for rent and utilities. the average cost for its products to be manufactured is about $3.00 an item. if the average price for a product sold in the store is $5.50, what will the break - even point be? let x represent the number of products sold. the break - even point occurs when the cost function equals the revenue function. 550 + 3.00x = 5.50x. naturally made needs to sell products to break even. the cost or revenue when it sells the break - even number of products will be $ .

the naturally made bath and body store pays $550 a month for rent and utilities. the average cost for its products to be manufactured is about $3.00 an item. if the average price for a product sold in the store is $5.50, what will the break - even point be? let x represent the number of products sold. the break - even point occurs when the cost function equals the revenue function. 550 + 3.00x = 5.50x. naturally made needs to sell products to break even. the cost or revenue when it sells the break - even number of products will be $ .

Answer

Explanation:

Step1: Solve for x in the break - even equation

We have the equation $550 + 3.00x=5.50x$. First, subtract $3.00x$ from both sides. $550+3.00x - 3.00x=5.50x - 3.00x$ $550 = 2.50x$

Step2: Find the value of x

Divide both sides of the equation $550 = 2.50x$ by $2.50$. $x=\frac{550}{2.50}=220$

Step3: Find the cost or revenue at break - even

Substitute $x = 220$ into the revenue function $R = 5.50x$ (we could also use the cost function). $R=5.50\times220 = 1210$

Answer:

Naturally Made needs to sell 220 products to break even. The cost or revenue when it sells the break - even number of products will be $1210.