Linear Programming Question

Question

Mary is considering two car-rental companies. Company A charges a rental fee of $20 and $0.59 per km. Company B charges a rental fee of $16 and $0.63 per km.

i) By constructing two linear functions for the fee charges of company A and B, calculate when does the charges are the same

ii) Decide when will the company A be the better choice for Kent and state the reason

I did (i) and got x=100 but i dont know how to proceed with (ii) please help

Answer 1

Let A and B be the charges for respective companies.

A=20+0.59k, B=16+0.63k where k is the distance in km.

(i) When A=B, 20+0.59k=16+0.63k, 4=0.04k, k=100km (as you thought), so the charge is 20+59=$79=16+63.

(ii) When A<B (A is the better choice because it's cheaper) 20+0.59k<16+0.63k, 4<0.04k, 100<k, so, when the distance is less than 100km, A is the better choice.