Take home Assignment counts as a quiz grade Due In class 7Ue

Take home Assignment (counts as a quiz grade) Due: In class, 7Uesday, Dec. 6 Table 1. The cost, in dollars, of a one-day truck rental is dependent on the number of miles driven. The cost to drive 40 miles is sss and the cost to drive 180 miles is s108. Assume the relationship between cost and les driven can be represented using a linear function. mi a. Find the slope. Show all work. b. What does the slope represent in the context of this problem? 2. The manufacturer of a dishwasher has found that when the unit price is p dollars, the 4p2 4000p revenue R (in dollars) is RO a. Determine the y intercept. Explain what this represents in the context of the problem. b. What is the domain, out of context, for this function? c. What is the domain, in context, for this function? d. what unit price should be charged for the dishwasher in order to maximize revenue? e. What is the maximum revenue?

Solution

1)let cost =y ,miles driven =x

2points on curve are (40,59),(180,108)

a) slope =(108-59)_/(180-40)

slope =49_/140

slope =7_/20

b) slope represent the change of cost in dollars per mile

================================================

2) R(p)=-4p²+4000p

R(p)=-4(p²-1000p)

R(p)=-4(p²-1000p+(1000_/2)²-(1000_/2)²)

R(p)=-4(p²-1000p+(1000_/2)²)+4(1000_/2)²

R(p)=-4(p-500)²+1000000

R(p)=-4(p-500)²+1000000

a)for y intercept , p=0

R(0)=-4*0²+4000*0

R(0)=0

y intercept represents revenue when no units are sold

b) domain is (-,)

c)domain (0,1000)

maximum numer of units that can be sold to generate the revenue(revenue cannot be less than zero)

d) vertex is (500,1000000)

500 dollars should be charged for maximum revenue

e)maximum revenue =1000000 dollars