3. A small-scale manufacturer has production facilities for producing two different products. Each of the products requires three different operations: grinding, assembly and testing. Product-I requires 15, 20 and 10 minutes to grind, assemble and test respectively whereas product-II requires 7.5, 40 and 45 minutes for grinding, assembly and testing. The production run calls for a least 7.5 hours of grinding time, at least 20 hours of assembly time, and at least 15 hours of testing time. If product-I costs $ 60 and product-II cost $90 to manufacture, determine the number of units of each product the firm should produce in order to minimize the cost of operations using Duality principle