Assume that producing 1 unit of coal requires 04 units of co

Assume that producing 1 unit of coal requires 0.4 units of coal, 0.3 units of lumber, and 0.2 units of steel; that producing 1 unit of lumber requires 0.1 units of coal, 0.2 units of lumber, and 0.3 units of steel; and that producing 1 unit of steel requires 0.8 units of coal, 0.1 units of lumber, and 0.4 units of steel.

Find the production schedule that satisfies an external demand for 56 units of coal, 23 units of lumber, and 14 units of steel.

X= [ , , ]

Solution

1 unit of coal = 0.4C+0.3L+0.2S

56 unis of coal = 56(0.4C+0.3L+0.2S) = 22.4C+16.8L+11.2S ...........(1)

1 unit of lumber = 0.1C+0.2L+0.3S

23 units of lumber = 23(0.1C+0.2L+0.3S) = 2.3C+4.6L+6.9S ...............(2)

1 unit of steel = 0.8C+0.1L+0.4S

14 units of steel = 14(0.8C+0.1L+0.4S) =11.2C+1.4L+5.6S .................(3)

Adding (1),(2) and (3) equations.

To produce 56 units coal , 23 units of lumber and 14 units of steel , we need 35.9 units of coal ,22.8 units of lumber and 23.7 units of steel.

X = [ 35.9 , 22.8 , 23.7 ]