The monthly demand equation for an electric utility company is estimated to be p = 76 - (10-5)x, where p is measured in dollars and x is measured in thousands of killowatt-hours. The utility has fixed costs of $9,000,000 per month and variable costs of $46 per 1000 kilowatt-hours of electricity generated, so the cost function is C(x) = 9• 106 + 46x. (a) Find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) Suppose that the rising fuel costs increase the utility's variable costs from $46 to $56, so its new cost function is C, (x) = 9• 106 + 56x. Should the utility pass all this increase of $10 per thousand kilowatt-hours on to the consumers? (a) Find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. x=0 (Type an integer or a decimal.) X =

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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.