A welder fabricates steel doors, gates, and tables using cutting and welding machines. He has 200 units of steel, 630 processing hours of cutting machine, and 600 hours of welding machine. He earns a profit of £750 from a door, £700 from a gate, and £800 from a table. The following table summarizes the resource requirements of the products.

The welder wants to determine the number of products of each type he needs to produce to maximize his profit.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.
c. Compare the solution with the solution you get with the integer restrictions relaxed and indicate whether the rounded down solution is optimal.

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Steel (units) Cutting hours Welding hours Door 5 14 10 Gate 4 16 12 Table 3 12 14