Matchpoint is considering producing a low-pressure ball, suited for high altitudes, called the special duty. Each gross of special duty balls would require 1 ½ and ¾ man-hours of manufacturing and testing, respectively, and would give a profit contribution of $33 per gross. Special duty balls would be packed in the same type of cans as the other balls. Should matchpoint produce any of the special duty balls? Explain; provide support for your answer.

Matchpoint company produces 3 types of tennis balls: heavy duty, regular, and extra duty, with a profit contribution of $24, $12, and $36 per gross (12 dozen), respectively. The linear programming formulation is: max. 24x1 + 12x2 + 36x3 subject to: .75x1 + .75x2 + 1.5x3 _ 300 (manufacturing) .8x1 + .4x2 + .4x3 _ 200 (testing) x1 + x2 + x3 _ 500 (canning) x1, x2, x3_ 0 where x1, x2, x3 refer to heavy duty, regular, and extra duty balls (in gross).