1313Day2 - Math 1313 Section 1.5 Section 1.5 Linear Models...

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Math 1313 Section 1.5 1 Section 1.5: Linear Models An asset is an item owned that has value. Linear Depreciation refers to the amount of decrease in the book value of an asset. The purchase price , also known as original cost , of an asset is the price paid for the asset when purchased. The scrap value of an asset is the remaining value after it is no longer seen as useable. Example 1: In 2010, the B&C Company installed a new machine in one of its factories at a cost of $150,000. The machine is depreciated linearly over 15 years with no scrap value. a. Find the rate of depreciation for this machine. b. Find an expression for the machine’s book value in the t-th year of use (0 < t < 15). Example 2: A company’s car has an original value of $85, 000 and will be depreciated linearly over 6 years with scrap value of $10,000. a. Find the expression giving the book value of the car at the end of year t (0 < t < 6). b. Find the car’s book value in at the end of the third year.
Math 1313 Section 1.5 2 Linear Cost, Revenue and Profit Functions: If x is the number of units of a product manufactured or sold at a firm then, The cost function , C(x), is the total cost of manufacturing x units of the product. Fixed costs are the costs that remain regardless of the company’s activity. Examples: building fees (rent or mortgage), executive salaries Variable costs are costs that vary with the production or sales. Examples; wages of production staff, raw materials The revenue function , R(x), is the total revenue realized from the sale of x units of the product. The profit function , P(x), is the total profit realized from the manufacturing and sale of the x units of product.

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