Find and describe how the rate at which the Profit П is changing per week, when the lamps are priced $59 each.?
A particular lamp that is to be sold at a small specialty store has $1000 in fixed costs and $3 per lamp in variable costs. The owners have spoken with a marketing expert that found that the linear demand of the lamp has a demand selling price of p = -6q + 305, where q is the demand quantity of lamps being sold.
The owners decide to decrease the price by $.84 each week.
Find and describe how the rate at which the Profit П is changing per week, when the lamps are priced $59 each.
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a POORLY worded query......a lamp did not have $1000 in fixed costs.....
C = 1000 + 3 q , R = p q = - 6 q² + 305 q....P = R - C = - 6 q² + 302 q - 1000...
dP/dt = [ - 12 q + 302 ] ( dq/dt)....p = 59 ===> 59 = - 6 q + 305 ===> q = 41
dP/dt = (- 190 ) ( - 0.84) = 159.00 dollars