Introduce slack variables as necessary, and then write the initial simplex tableau for each linear programming problem.
1). Find x1 ≥ 0 and x2 ≥ 0 such that
X1 + x2 ≤ 10
5x1 + 3x2 ≤ 75
and z = 4x1 + 2x2 is maximized
2. Production -Knives The Cut-Right Company sells set of kitchens knives. The Basic Set consists of 2 utility knives and 1 chef's knife. The Regular Set consists of 2 utility knives. 1 chef's knives and 1 slicer . Their profit is $30 on a Basic Set, $40 on a Regular Set, and $60 on a Deluxe Set. The factory has on hand 800 utility knives,400 chef's knives, and 200 slicers. Assuming that all sets will be sold, how many of each type should produced in order to maximize profit? What is the maximum profit?
3). Maximum z= 12x1 + 15x2 + 5x3
Subject to 2x1 + 2x2 + x3 ≤ 8
X1 + 4x2 +3x3 ≤ 12
With x1≥ 0, x2≥ 0, x3≥ 0.
1) If you work out the solution by hand or with Excel(spreadsheet), you'll find that in order to maximize Z, x1 = ...