South West Electronics Corporation (SWEC) designs high-tech business and residential security systems. The company's marketing analyst has been assigned to analyze market demand for SWEC's top-selling system, The Terminator. Monthly demand for The Terminator has been estimated as follows:
q = 445 - 8p + 25A + 4.5C + 6Y
where q = Expected number of system sales per month
p = Selling price for The Terminator (in dollars)
A = Advertising (in thousands of dollars)
C = SWEC,s only competitor's average price (in dollars)
Y = Disposable annual per capita income (in thousands of dollars)
A recent survey of the potential customer market indicates that monthly advertising is $25,000, per capita disposable income is $80,000 per year, and the average price of the only competitor is $100.
(a) Based on this information, what is the monthly demand function p=f (q) for The Terminator?
(b) Find the elasticity of demand for The Terminator.
(c) If SWEC's current price for The Terminator is $175, is demand elastic, inelastic, or unitary elastic? Is SWEC's revenue for The Terminator maximized at the current price?
(d) Use the elasticity of demand found in part (b) to determine the price for The Terminator that would maximize SWEC's revenue. Find the maximum revenue.