3.B.1 Example 3-1: Homewood Masonry-A Materials Production Problem Problem Statement. Homcwood Masonry is a small owner-operated firm that produces construction materials for the residential and commercial construction industry in the region. The company specializes in the manufacture of two widely used building products: (1) a universal concrete patching product called HYDIT and (2) a decorative brick mortar called FILIT. These products are in great demand, and Homewood can sell all of the HYDIT it produces for a profit of $140 per ton. and all the FILIT' it can produce for a profit of $160 per ton. Unfortunatcly, some of the resources needed to manufacture these products are in limited supply. First, the demand for both HYDIT and FILIT is due in large part to their special adhesive characteristics, which result from the use of a special ingredient in the blending process-Wabash Red Clay (from the banks of the Wabash River in Indiana). Each ton of HYDIT produced requires 2 cubic meters of this red clay. and each ton of FILIT produced requires 4 cubic meters. Wabash Red Clay is in limited supply; a maximum of 28 cubic meters of the clay is available each week. Second. the operator of the machine used to blend these products can work only a maximum of 50 hours per week. This machine blends a ton of either product at a time, and the blending process requires 5 hours to complete. Last. each material must be stored in a separate curing vat, further limiting the overall production volume of each product. The curing vats for HYDIT and FILIT have capacities of 8 and 6 tons. respectively. These resource limitations are summarized in Table 3.1. TABLE 3.1 RESOURCE REQUIREMENTS AND AVAILABILITY FOR THE HOMEWOOD MASONRY PROBLEM Mathematical Modelling and Linear Programming Problem 1 For the Homewood Masonry optimization problem, (1-1) draw a figure showing the feasible region. In class, we started with 1 as the first variable to become basic and we used simplex to update the solution by moving from one corner to the next corner until the optimum point was obtained. Show the corners on the figure and show the path from the initial point to the final point. (1-2) Solve the same problem again but this time start with x2 instead of x1. Do not use the tabular form and follow the steps according to lecture note 3 that was discussed in class and is posted on moodle too. (1-3) Solve part (1-2) using simplex tables, starting from 2. (1-4) Similar to part (1-1), show the path of simplex solution, starting from 2, to the optimum point