To determine the number of containers that can be shipped, we need to set up a system of equations using the given constraints. By graphing the feasible region and finding the vertices, we can determine the maximum values for the number of 5-pound and 10-pound containers. In this case, the maximum values are 2 5-pound containers and 7 10-pound containers.
To determine the number of 5-pound and 10-pound containers of coffee that can be shipped within the given size limit, we can set up a system of equations. Let's say x represents the number of 5-pound containers and y represents the number of 10-pound containers.
The volume constraint can be represented by the equation: 36x + 12y ≤ 108. The weight constraint can be represented by the equation: 5x + 10y ≤ 50. We can now solve this system of equations to find the possible values of x and y.
By graphing the feasible region, we can determine the possible combinations of 5-pound and 10-pound containers that satisfy both constraints. The vertices of the feasible region represent the maximum values of x and y that can be used.
For example, if we use 3 5-pound containers and 1 10-pound container, the total volume would be 36(3) + 12(1) = 132 cubic inches, which is higher than the limit of 108 cubic inches. Therefore, the maximum values for x and y that satisfy both constraints are x = 2 and y = 7.