You are the sales manager for Montevideo Productions, Inc., and you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,500. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 35 contracts. This is down 10 contracts from the figure last year, when your company charged only $2,000. Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo Productions, Inc., charges for development.
A) $q = - 50 p - 85$
B) $q = - 0.02 p - 85$
C) $q = - 0.02 p + 85$
D) $q = 50 p + 85$
E) $q = 0.02 p + 85$

Question

You are the sales manager for Montevideo Productions, Inc., and you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,500. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 35 contracts. This is down 10 contracts from the figure last year, when your company charged only $2,000. Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo Productions, Inc., charges for development. 
A) $q = - 50 p - 85$
B)   $q = - 0.02 p - 85$
C)  $q = - 0.02 p + 85$
D)  $q = 50 p + 85$
E)  $q = 0.02 p + 85$

Quizplus · Accepted Answer

To construct a linear demand equation $q = mp + b$, we need to find the slope $m$ and the y-intercept $b$. The slope can be calculated using the change in quantity ($\Delta q$) over the change in price ($\Delta p$). From the information given, when the price increased from $2,000 to $2,500 (a change of $500), the number of contracts decreased from 45 to 35 (a change of -10 contracts). Thus, the slope $m = \frac{\Delta q}{\Delta p} = \frac{-10}{500} = -0.02$.To find the y-intercept $b$, we can use one of the given points. Using the point ($2,500, 35), we substitute into the equation $q = -0.02p + b$ to solve for $b$:$35 = -0.02(2500) + b$$35 = -50 + b$$b = 85$Therefore, the linear demand equation is $q = -0.02p + 85$.

You Are the Sales Manager for Montevideo Productions, Inc q=−50p−85q = - 50 p - 85q=−50p−85

You Are the Sales Manager for Montevideo Productions, Inc $q = - 50 p - 85$