The Township Machine Company is planning to add a new product line and wishes to hire some experienced

machinists. The local union hall has advised Township that machinists are categorized in one of two skill levels:

normal, and apprentice. A normal machinist must have 6 years of experience and should produce 16 pieces a day. An

apprentice machinist must have at least a year of experience and should produce 12 pieces a day. The Township

Company's union contract calls for wage scales of Php 600, Php 400 per day for the two skill levels. Currently, there

are at most 10 normal machinists, and 11 apprentice machinists available for hire. Township has budgeted Php 40,000

a week (5-day week) for machinists' salaries for the manufacture of its new product. Township would like to hire a

complement of new workers which will yield the highest output rate, but would like to keep both the union and

present employees happy by ensuring that the total experience of the workers hired represents a seniority level of at

least 60 worker-years. Formulate the linear programming model which will find the number of machinists of each

category that Township should hire to maximize its expected output rate, and solve the problem using the graphical

method.