Problema Solution
A company produces doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets.
Answer provided by our tutors
let 'x' represent the number of doll houses produced and 'y' represent the number of furniture sets produced
labor for doll houses:
3x
labor for furniture sets:
8y
let 'T' represent the total number of items produced in a week, then we are limited to 100 items per week:
T <= 100
we need at least 20 doll houses and 10 furniture sets, so:
T >= 20x + 10y
labor can not exceed 400 hours per week:
400 >= 3x + 8y
so our system of inequalities becomes:
100 >= 20x + 10y
400 >= 3x + 8y