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MATH 110 BUSINESS CALCULUS CHAPTER 1 FUNCTIONS AND LINEAR MODELS Section 1.4 Linear Models A linear model is a linear function which can be used to describe or approximate relationships in the real world. In our course we start by using linear functions to model cost , revenue , and profit . In business, a cost is the value of money that has been used up to produce something. Here is the linear model for the cost C as a function of the number of items x : C(x) = mx + b b is fixed cost , mx is variable cost , and m is marginal cost (cost per item). Example : A piano manufacturer has a daily fixed cost of \$1200 and a marginal cost of \$1500 per piano. Find the cost C(x) of manufacturing x pianos in one day. On a given day, what is the cost of manufacturing 3 pianos? Solution : The cost function is C(x) = 1500x + 1200. The cost of manufacturing 3 pianos is C(3) = 1500(3) + 1200 = \$5,700

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In business, revenue or revenues is income that a company receives from its normal business activities, usually from the sale of goods and services to customers. Here is the linear model for the revenue
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