A roofing contractor purchases a shingle delivery truck with a shingle elevator for $37,800. The vehicle requires an average expenditure of $9.50 per hour for fuel and maintenance, and the operator is paid $13.50 per hour. (a) Write a linear equation giving the total cost C of operating this equipment for t hours. (Include the purchase cost of the equipment.) C(t) =        (b) Assuming that customers are charged $44 per hour of machine use, write an equation for the revenue R obtained from t hours of use. R(t) =        (c) Use the formula for profit  P = R − C  to write an equation for the profit obtained from t hours of use. P(t) =        (d) Use the result of part (c) to find the break-even point—that is, the number of hours this equipment must be used to yield a profit of 0 dollars. t =  hr

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.