Question

A car company makes 2 types of cars: luxury and sport. Each luxury car costs the company $15,000 for parts and requires 1,600 man-hours to build. Each sport car costs the company $16,000 for parts and requires 1,500 man-hours to build. In a given month, the company allocated 61,500 man-hours and invested $625,000 in parts. How many of each type of car did the company make in this month?

Answer 1

luxury=15

sports cars 25

Explanation:

Step one:

let the luxury cars be x

and the sports cars be y

the objective function is

maximize

15000x+16000y=625000------1

the constraints are

1. Man-hours

1600x+1500y=61500-----------2

Step two:

the system of equation for the situation is

15000x+16000y=625000------1

1600x+1500y=61500-----------2

let us reduce both equation

divide equation 1 be 1000

and equation 2 by 100 we have

15x+16y=625--------1 x15

16x+15y=615--------2 x16

225x+240y=9375

-256x+240y=9840

=-31x+0=-465

31x=465

x=465/31

x=15

put x=15 in 15x+16y=625 we have

15(15)+16y=625

225+16y=625

16y=625-225

16y=400

y=400/16

y=25