Mathematical M&delling an;.l Linear Programming A small manufacturer of concrete slabs produces two types of slabs. It wants to determine how many slabs of each type (X1 of type 1 and X2 of type 2) to produce over the coming period to maximize profit. Each type of slab passes through three manufacturing processes (A, B, and C). Information related to the required hours for manufacturing and the available man-hour for each process is as follows: Slab type 1 needs 2 man-hours of process A, 3 hours of process B and 1 hour of process C while slab type 2 needs 5 hours of process A, 1 hours of process B and 1 hour of process C. The profits from manufacturing and selling the slabs are: 2 S/slab type 1 and 1 $/slab type 2. The total man-hour available for the processes are: (A, 60 hr), (B, 44 hr) and (C, 18 hr). The market research team in the company dictates that at most (no more than) 10 standard slabs of X2 type could be produced over the coming period. (i) Tabulate the data; (ii) Develop a linear programming model that will enable the company to maximize its profit; (iii) Find the optimal solution using graphical method, (iv) Find the optimal solution if the profits were: 1 $/slab type 1 and 3 $/slab type 2