Hint: Reverse the signs and ignore entries of 0 and 1. The Kaolene Co. Ltd has six different products all made from fabricated steel. Each product passes through a combination of five production operations: cutting, forming, drilling, welding and coating.
Steel is cut to the length required, formed into the appropriate shapes, drilled if necessary, welded together if the product is made up of more than one part, and then passed through the coating machine. Each operation is separate and independent, except for the cutting and forming operations, when, if needed, forming follows continuously after cutting. Some products do not require every production operation.
The output rates from each production operations, based on a standard measure for each product, are set out in the tableau below, along with the total hours of work available for each operation. The contribution per unit of each product is also given. It is estimated that three of the products have sales ceilings and these are also given below:

The production and sales for the year were found using a linear programming algorithm. The final tableau is given below. Variables X7 to X11 are the slack variables relating to the production constraints, expressed in the order of production. Variables X12 to X14 are the slack variables relating to the sales ceilings of X3, X5 and X6 respectively.
After analysis of the above results, the production manager believes that further mechanical work on the cutting and forming machines costing £200 can improve their hourly output rates as follows:

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Products Contribution per Output rate per hour X1 3 X5 X6 unit (E) 5.7 10.1 12.3 9.8 17.2 14.0 Cutting Foming Drilling Welding Coating 650 450 700 450 200 370 450 520 300 420 180 380 300 400 720 600 450 380 380 670 540 480 500 Maximum sales units (000) 150 _ 20 70 Cutting Forming Ding Welding Coating Production hours available 12000 16000 4000 4000 16000 Products X1X2 X3 X4 X5 X6 Cutting 700 770 410 500 330 470 Forming 540 540 620 220 460