Question

A company manufactures Handband, a wireless activity tracker. There are initial start-up costs involved. Additionally, the company spends a certain amount of money to manufacture each Handband. The cost of manufacturing & Handbands is given by the function, C(h) = 21h + 15000. Which of the following statements are true? Check all that apply.

O If the initial start-up costs are not considered, the value 21 is the cost to make one Hadband.
O The value 15000 represents the average number of Handbands manufactured each year.
O The value 15000 represents the start-up cost.
O The function C(h) represents the revenue the company receives from the sales of Handbands.
O The company spends $57,000 to manufacture 2000 Handbands.
O The company earns $21 profit for each Handband they sell

Answer 1

The correct answer are 1,3 and 5. The cost function C(h) outlines the total cost to produce Handbands, where 21 is the variable cost per unit and 15000 is the fixed start-up cost. True statements include the unit cost being $21 without start-up costs and the company spending $57,000 to produce 2000 Handbands. Claims about average manufacture numbers, revenue, or profit margin based on this function are incorrect.

Step-by-step explanation:

The cost function for manufacturing Handbands, C(h) = 21h + 15000, outlines the total cost of production for h Handbands. Analyzing the function allows us to evaluate the provided statements and deduce which are true.

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• If the initial start-up costs are not considered, the value 21 represents the cost to manufacture one Handband. This is indeed true since the variable cost associated with each additional unit produced is the coefficient of h in the function.
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• The value 15000 represents the fixed start-up cost, which is also true. It indicates the cost incurred before any Handbands are produced.
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• As for the claim that the company spends $57,000 to manufacture 2000 Handbands, substituting h = 2000 into the function C(h) yields C(2000) = 21*2000 + 15000, which does calculate to $57,000.

The other provided statements are incorrect:

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• The value 15000 does not represent the average number of Handbands manufactured each year; it indicates the initial costs.
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• The function C(h) does not represent revenue, but the total cost of production.
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• The company doesn't necessarily earn $21 profit for each Handband they sell, since the function only covers the cost of production, not the selling price.