Problema Solution
A company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. The cost of labor to manufacture a mountain bike is $90, and the cost of labor to manufacture a trail bike is $30. During a week in which the company has budgeted $1,400 for materials and $2,250 for labor, how many mountain bikes does the company plan to manufacture?
Answer provided by our tutors
let
x = the number of mountain bikes, x>= 0, x is integer
y = the number of trail bikes, y>=0, y is integer
The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. The company has budgeted $1,400 for materials:
40x + 40y <= 1400 divide both sides by 40
x + y <= 35
The cost of labor to manufacture a mountain bike is $90, and the cost of labor to manufacture a trail bike is $30. The company has budgeted $2,250 for labor:
90x + 30y <= 2250 divide both sides by 30
3x + y <= 75
by solving the system
x + y = 35
3x + y = 75
we find:
x = 20 mountain bikes
y = 15 trail bikes
click here to see the step by step solution of the system of equations:
if we assume that the company spends all the budget for materials and labor the company plans to manufacture 20 mountain bikes.