local retailer has determined that the number of portaBoy ga

local retailer has determined that the number of portaBoy game systems sold in a week, x, is related to the price of each system, p, in dollars. (a) In response to economic forces, the local retailer set the selling price at s250, and 30 game systems were sold each week. When the systems went on sale $220 the following week, 40 units per week were sold. Find a linear function which fits this data. Use the weekly sales,x, as the independent variable and the price, p, as the dependent variable. (i) Find a suitable applied domain. [113 113) [0, co) O [0, 113] O (-00, 113] (-oo, oo) (ii) Interpret the slope. Since the slope is Select B, we have that the price is decreasing at a rate of per PortaBoy sold. (iv) If the retailer wants to sell 180 PortaBoys next week, what should the price be? Does this answer make sense? (v) What would the weekly sales be if the price were set at $180 per system? (Round your answer to the nearest whole number) PortaBoys (b) The revenue of selling x units at a price p per unit is given by the formula R xp. Find and simplity an expression for the weekly revenue R as a function of weekly sales, x.

Solution

p -- price varible and x -- no.fo games

we have two points ( x, p) = ( 30 , 250) and (40, 220)

slope = ( 220 -250)/( 40 -30) = -30/10 = -3

p = -3x +c ; 250 = -90 +c ; c = 340

p = -3x + 340   xintercept : ( 113.33 ,0) and y intercept : ( 0, 340)

So, Domain : (0, 113.3)

Slope means : It means when games sold increases by 1 the price of games system decreases by $ 3

when x= 180 prta boys ;p( 180) = -3*180 + 340 = - $200

No, the answer does not make sense