There are two laundry trucks One laundry truck visits Roxanne's house every 3 days and another laundry truck visits her neighbor
1 answer:
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Answer:
a)q(p)=-15p+ +300
b)R(p)=-15p²+300p
c)C(p)=-30p+1600
d.1)P(p)=-15p²+330p-1600
d.2)p=$11
Step-by-step explanation:
(a).Before getting started, we are going to consider the cartesian plane, where x-axis corresponds to the cover charge and y-axis corresponds to number of guests per night . There, we will locate the following coordinates according to the previous information:
(9,165) (10,150).
Remember that the slope-intercept form of the linear equation is y=mx+b where m is the slope and b is te intercept.
The slope can be calculated by the next formula:
In this case we will assign (9,165) as the first coordinate and (10,150) as the second one. The order does not matter. At the end we get the same value for m.
Therefore:
Now, we have the slope and two poitns. According to this, and taking into account that point-slope form of the equation of a line is y-y1=m(x-x1), find a linear demand equation.
Any of two coordintates can be selected. In this case we will select the second one.
y-150=-15(x-10) equation 1
Solve equation 1 for y
y=-15x+150+150
y=-15x+300
Above we had defined x as cover charge (p) and y as number of guests (q). Thus, rewrite equation 1.
q(p)=-15p+ +300.
it equation shows the number of guests per night as a function of the cover charge,
(b). The nightly revenue can be calculated multplying the price of the cover charge by the number of guests. So, we just have to multiply the equation 1 by p.
p*q(p)=p*(-15p +300)
R(p)=-15p²+300p equation 2
(c) To get the cost function of the nightclub we just have to multiply the cost of the two non-alcoholic drinks by the number of the guests ( equation 1) and add to it nightly overheads.
C(p)=2*(-15p+300)+1000
C(p)= -30p+600+1000
C(p)=-30p+1600 equation 3
(d) In order to find the profit in terms of the cover charge we will subtract nightly costs ( equation 3) from nightly revenue (equation 2)
P(p)=R(p)-C(p)
P(p)=-15p²+300p - (-30p+1600)
P(p)=-15p²+300p+30p-1600
P(p)=-15p²+330p-1600
To determine that the entrance fee we should charge for a maximum profit we are going to use the first derivative test (y'(x)=0) in order to find an extremum point.
Compute the first derivative of P(p)
P'(p)=-30p+330=0
30p=330
p=330/30
p= $11
The entrance fee that we should charge for a maximum profit is p=$11 per guest.
Answer:
(a). $1465.42
(b). $214.58
Step-by-step explanation:
We have been given that installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. The interest rate is 1.25% per month on the unpaid balance.
(a) To find the cost of the TV, we will use monthly payment formula.
, where,
R = Periodic payment,
P = Loan amount,
i = Monthly interest rate in decimal form,
n = Number of total payments.
We know that total cost of TV would be equal to down payment plus amount of loan that is:
Therefore, the total cost of the TV would be $1465.42.
(b). First of all, we need to find total amount paid in 3 years by multiplying amount of each monthly payment by 36 (3 years equal to 36 months).
To find the total amount of interest paid, we will subtract amount of loan from total payment.
Therefore, the total amount paid in interest would be $214.58.
Answer:
Increasing:
Decreasing:
Step-by-step explanation:
So when an equation has and odd degree, it will go in the opposite direction on both ends, so if y went towards infinity as x went towards infinity, then y would go towards negative infinity as x goes towards negative infinity. In this case, by looking at the graph it has an odd degree, due to opposite end behaviors, although on both ends it's increasing because even though it appears that it's going down on the left side, that's only if you start from the right and go towards the left. So it's really increasing from negative infinity to -1, and then it decreases from -1 to 2, until it once again starts increasing from 2 to infinity. This can be represented as (-infinity, -1) U (2, infinity) for increasing and (-1, 2) as decreasing