A real estate office manages an apartment complex with 50 units. When the rent is $760 per month, all 50 units are occupied. However, when the rent is $799, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear. (Note: the term demand refers to the number of occupied units.)(a) Write a linear equation giving the demand x in terms of the rent p. x(p) = .(b) Use a graphing utility to graph the demand equation and use the trace feature to predict the number of units occupied if the rent is raised to $835. units(c) Predict the number of units occupied if the rent is lowered to $802. Verify graphically. units

The monthly demand equation for an electric utility company is estimated to be p equals 60 minus left parenthesis 10 superscript negative 5 baseline right parenthesis x, where p is measured in dollars and x is measured in thousands of killowatt-hours. the utility has fixed costs of $3 comma 000 comma 000 per month and variable costs of $32 per 1000 kilowatt-hours of electricity generated, so the cost function is upper c left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 32 x. (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 $32 to $38, so its new cost function is upper c 1 left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 38 x. should the utility pass all this increase of $6 per thousand kilowatt-hours on to the consumers?