John manufactures household furniture. His start-up costs, including tools, plans, and advertising, total $5000. Labor and materials for each piece of furniture total $350, and his production costs are the sum of his start-up costs plus the cost of labor and materials. If John makes f pieces of furniture, what will be his production costs, c, in dollars? Choose 1 answer: (A) f=350 c+5000 (B) c=350 f+5000 (C) f=5000 c+350 (D) c=5000 f+350

Question

John manufactures household furniture. His start-up costs, including tools, plans, and advertising, total  $5000. Labor and materials for each piece of furniture total  $350, and his production costs are the sum of his start-up costs plus the cost of labor and materials. If John makes  f pieces of furniture, what will be his production costs,  c, in dollars? Choose 1 answer: (A)  f=350 c+5000 (B)  c=350 f+5000 (C)  f=5000 c+350 (D)  c=5000 f+350

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Identify variables: Identify the variables and their meanings. John's start-up costs are a fixed amount of $5000. This is a one-time cost. The cost of labor and materials for each piece of furniture is $350. John's production costs, c, will be the sum of his start-up costs and the cost of labor and materials for f pieces of furniture.Write equation: Write an equation to represent the total production costs. The production costs are the sum of the start-up costs and the cost of labor and materials for each piece of furniture. The cost of labor and materials for each piece of furniture is multiplied by the number of pieces, f. So, the equation for the production costs is c = start-up costs + (cost per piece * number of pieces).Substitute values: Substitute the given values into the equation. The start-up costs are $5000, and the cost per piece is $350. Substituting these values into the equation from Step 2 gives us c = 5000 + (350 * f).Simplify equation: Simplify the equation. The equation c = 5000 + (350 * f) is already in its simplest form. This equation represents the total production costs, c, for f pieces of furniture.Match with answer choices: Match the equation with the given answer choices. The correct equation is c = 5000 + (350 * f). This matches with answer choice (B) c = 350f + 5000.

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