a company manufactures three product X,Y and Z. the sales volume for X is at least 50% of the total sales of all three products. however, the company cannot sell more than 80 units of X per day. the three products use one raw material, of which the maximum daily availability is 240 lb. the usage rates of the material are 2 lb per unit of X, 4 lb per unit of Y and 3 lb per unit of Z. the unit prices for X,Y and Z are $20, $50 and $35 respectively.
a) formulate a mathematical model for the problems
b) determine the optimal mix for the company
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