we run a company that produces small paper - based products - badges, decals, etc. - for events such as the…

we run a company that produces small paper - based products - badges, decals, etc. - for events such as the world series. to produce each item costs us one dollar. we also pay an initial startup cost for production of one hundred sixty dollars, regardless of the number of products that we produce. we plan to sell each product for five dollars.\ndefine units for the cost of making products and the income from the sale of products. enter a variable for the number of products and use this variable to write expressions for the cost of making products and the income from the sale of products.\n1. what is our initial cost of production? what is our initial income?\n2. how much would the cost be to produce 140 products? what is our income if we sell 140 products?\n3. if our income was nine hundred fifty dollars, how many products did we sell?

we run a company that produces small paper - based products - badges, decals, etc. - for events such as the world series. to produce each item costs us one dollar. we also pay an initial startup cost for production of one hundred sixty dollars, regardless of the number of products that we produce. we plan to sell each product for five dollars.\ndefine units for the cost of making products and the income from the sale of products. enter a variable for the number of products and use this variable to write expressions for the cost of making products and the income from the sale of products.\n1. what is our initial cost of production? what is our initial income?\n2. how much would the cost be to produce 140 products? what is our income if we sell 140 products?\n3. if our income was nine hundred fifty dollars, how many products did we sell?

Answer

Explanation:

Step 1: Encontrar el costo inicial y la ganancia inicial

El costo de producción se da por la expresión (160 + x). Cuando (x = 0) (costo inicial, sin producir nada), el costo es (160+0 = 160) dólares. La ganancia se da por la expresión (5x). Cuando (x = 0) (ganancia inicial, sin vender nada), la ganancia es (5\times0=0) dólares.

Step 2: Calcular el costo y la ganancia para (x = 140)

Para el costo, sustituimos (x = 140) en (160 + x): (160+140 = 300) dólares. Para la ganancia, sustituimos (x = 140) en (5x): (5\times140 = 700) dólares.

Step 3: Encontrar (x) cuando la ganancia es (950) dólares

Dado que la ganancia se expresa como (5x) y la ganancia es (950) dólares, resolvemos la ecuación (5x=950). Dividiendo ambos lados por (5): (x=\frac{950}{5}=190).

Answer:

  1. Costo inicial: (160) dólares, Ganancia inicial: (0) dólares.
  2. Costo para (140) productos: (300) dólares, Ganancia para (140) productos: (700) dólares.
  3. Número de productos vendidos: (190).