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1. A proposal was made to add another machine that could add 8 hours per day to machine availability. The machine would PhP200,000 and have a useful life of 5 years. There are 250 working days in a year. Annual maintenance costs amount to PhP100,000. Would this be a good investment if the cost of capital is 20%?
2. By how much can variable cost be decreased in Process III so that it enters the optimal mix?
3. To ensure that all items produced from these processes are of good quality, the company set up a quality process that will check outputs of the five processes. One worker was assigned to perform quality checks to all products produced by all processes. The checker will work for 8 hours a day. The time needed to check a unit of each product varies as shown from the table.

Can the checker be able to finish checking the daily production? If not, what will be the new optimal solution?

A firm can produce 3 products (A, B, C) using anyone of five different processes (I, II, III, IV, and V). The table below summarizes the yields of A, B, and C from one batch started in each process. The selling prices of each product, the skilled labor required to complete a batch, and the variable cost of completing a batch by each process are shown. Due to a contract requirement the company must produce at least 110 units of product A/day. The optimal solution for the problem: xB=x1x2x5=26168xN=x3x4S1S2S3b=1108050B=301241021N=462411100010001CB=(203045)CN=(405000)B1=1/51/52/51/53/101/102/53/56/5CBB1NCN=(1915/281/244)z=1360 Let xi= number of batches started in process i(i1 to 5) S1= surplus variable for the daily production requirement for product A S2,S3= slack variables for Skilled Labor and Machine Time, respectively \begin{tabular}{|c|c|c|c|c|c|} \hline Process & I & II & III & IV & V \\ \hline Time (mins.) & 11 & 8 & 6 & 5 & 10 \\ \hline \end{tabular}