Unit 1: Properties of Linear \[ \begin{array}{l}\text { Cost Function The simplest cost function is the linear cost function } \mathrm{C}(\mathrm{x})=\mathrm{mx}+\mathrm{b} \text {, where } \\ \text { the } y \text {-intercept b represents the fixed cost of operating a business and the slope } \mathrm{m} \\ \text { represents the variable costs. Suppose that a small bicycle manufacturer has daily fixed } \\ \text { costs of } \$ 1800 \text { and each bicycle costs } \$ 70 \text { to manufacture. } \\ \text { (a) Write a linear function that expresses the cost of manufacturing } \mathrm{x} \text { bicycles in a day. } \\ \mathrm{C}(\mathrm{x})=\square \\ \text { (Type your answer in slope-intercept form. Use integers or fractions for any numbers in }\end{array} \]

C(x) = 70x + 1800 To break it down, the fixed costs of $1800 contribute to the base cost regardless of the number of bicycles produced. Each additional bicycle increases the cost by $70, which is the variable cost associated with production. Hence, in total, the cost of manufacturing x bicycles in one day can be captured in this straightforward linear function! Your bicycle manufacturing journey doesn't end with just crafting bikes; consider the future of sustainable materials! Many innovative companies are exploring eco-friendly options, including recycled materials and lightweight composites, which not only support environmentally friendly practices but also cater to a growing market of eco-conscious consumers. Exploring this avenue could help your business stand out while contributing positively to the planet!