Problema Solution
Consider a company that specializes in potting soil. Each bag of potting soil for seedlings requires 2 units of sand, 1 unit of loam, and 1 unit of peat moss. Each bag of potting soil for general potting requires 1 unit of sand, 2 units of loam, and 1 unit of peat moss. Each bag of potting soil for hardwood plants requires 2 units of sand, 2 units of loam, and 2 units of peat moss. Find the numbers of bags of the three types of potting soil that the company can produce with the given amounts of raw materials.
950 units of sand
900 units of loam
650 units of peat moss
soil for seedlings _____bags
soil for general potting _____bags
soil for hardwood plants _____bags
Answer provided by our tutors
let
x = number of bags of potting soil for seedlings
y = number of bags of potting soil for general potting
z = number of bags of potting soil for hardwood plants
thus we can use
sand: 2x + y + 2z <= 950
loam: x + 2y + z <= 900
peat moss: x + y + 2z <= 650
by solving the system of inequalities
2x + y + 2z <= 950
x + 2y + z <= 900
x + y + 2z <=650
we find
x <= 300
y <= 250
z <= 50
soil for seedlings 300 bags
soil for general potting 250 bags
soil for hardwood plants 50 bags