# Length and Formula Word Problem

The cost formula for a manufacturer’s product is C = 5000 + 2 x , where C is the cost (in dollars) and x is the number of units manufactured. (a) If no units are produced, what is the cost?

(b) If the manufacturer produces 3000 units, what is the cost? (c) If the manufacturer has spent $16,000 on production, how many units were manufactured? Answer these questions by substituting the numbers into the formula. (a) If no units are produced, then x = 0, and C = 5000 + 2 x becomes C = 5000 + 2(0) = 5000. The cost is $5,000. (b) If the manufacturer produces 3000 units, then x = 3000, and C = 5000 + 2 x becomes C = 5000 + 2(3000) = 5000 + 6000 = 11,000. The manufacturer’s cost would be $11,000. (c) The manufacturer’s cost is $16,000, so C = 16,000. Substitute C = 16,000 into C = 5000 + 2 xto get 16,000 = 5000 + 2 x .

There were 5500 units produced.

Profit Formula Word Problem

The profit formula for a manufacturer’s product is P = 2 x – 4000 where x is the number of units sold and P is the profit (in dollars). (a) What is the profit when 12,000 units were sold?

(b) What is the loss when 1500 units were sold?

(c) How many units must be sold for the manufacturer to have a profit of $3000? (d) How many units must be sold for the manufacturer to break even? (This question could have been phrased, “How many units must be sold in order for the manufacturer to cover its costs?”) (a) If 12,000 units are sold, then x = 12,000. The profit equation then becomes P = 2(12,000) – 4000 = 24,000 – 4000 = 20,000. The profit is $20,000. (b) Think of a loss as a negative profit. When 1500 units are sold, P = 2 x – 4000 becomes P = 2(1500) – 4000 = 3000 – 4000 = – 1000. The manufacturer loses $1000 when 1500 units are sold. (c) If the profit is $3000, then P = 3000; P = 2 x – 4000 becomes 3000 = 2 x – 4000.

A total of 3500 units were sold.

(d) The break-even point occurs when the profit is zero, that is when P = 0. Then P = 2 x – 4000 becomes 0 =...

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