2. You are told that the price of an automobile depends on the following variables:
a) The number of passengers it can carry. (P)
The number of safety features it has. (S)
c) Its roominess (leg room, cargo space, etc.) (R)
d) Its fuel consumption. (F)
e) Its general annual maintenance cost (oil changes, part replacements, etc.) (M)
Answer the following questions:

i) Indicating your notation, write this information first as a general function
and then as a linear function.
ii) Comment on the likely sign of the coefficients in your linear function.
Briefly explain your answer.

So i dont remember general and linear functions i think linear is like slope C=Ax+B (y=mx+b)

but what is general just a regular function

So General: Price= P+S+R-F-M?
Linear: Price= P*R+S-M-F

If anyone could help me im confused af

I got another one, By the way i can pay if thats what people are waiting for.


A monopolist has a total cost function TC = 20q + 350, where q is output. Suppose the
demand function for the monopolist’s product is given by p = 100 – 2q, where p is
price. Government regulations require this firm to charge a price equal to average cost.
How many units could the firm produce in order to comply with this requirement?

So; TC = 20q + 350, p = 100 – 2q, AC=TC/Q

P=TC/Q

100-2q = 20 + 350/q
80 = 350/q+2q

How do i resolvyse with a /q and a q wont i always have Q^2 and q or q and /q

for question 2...

not sure if helps or if right, but i tried this a different way.
100-2q = 20 + 350/q
q(100-2q) = (20 + 350/q)q --> 100q-2q^2=20q+350

0=2q^2-80q+350 ----> 0=2(q^2-40q+175) ---> 0=2(q-5)(q-35) -----> q= 5 or 35
or
0=2q^2-80q+350 ----> 0=(2q-10)(q-35) or 0=(2q-70)(q-5) so i got q could equal 5,10,35,70

Wouldnt those be 5,35 since 70 and 10 are off the 2q?


To be honest im still confused but may use this and pray for part marks ty for help man!

Think general would be more like

Price = f(P,S,R,F,M) as in price is a function of P, S, R, F, and M and the function could be anything, for example Price = PR + S^2 - F^3/M, not necessarily only a linear function
As a linear function it can be something like Price = 2P + 3S + R - 2F - 2M, not sure if what you have is okay, linear means the highest degree is 1

I already sumbitted but for education's sake would the example you gave "Price = PR + S^2 - F^3/M" Have a degree higher than 1 as S is to the 2?

Yes

Price= P*R+S-M-F also has degree 2 because P and R are variables