A company has the choice of producing up to four different products with its machinery, which consists of lathes, grinders, and milling machines. The number of hours on each machine required to produce a product is given in the following table, along with the number of hours available per week on each type of machine. Assume that the company can sell everything it produces. The pro t per item for each product appears in the last line of the table.

a. Determine how many units of each product the company should make to maximize its total pro t, and then compute this profit. Remember, the company cannot make fractional units, so your answer must be in integers. First estimate the upper limits on the number of products that can be produced without exceeding the available capacity.

b. How sensitive is your answer? How much does the pro t decrease if you make one more or one less item than the optimum?

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Product 2 3 4 Hours available Hours required Lathe 1 0.5 3 40 Grinder 4 1 30 Milling Unit pro t ($) 3 1 5 45 100 150 90 120