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 0 where x1, x2, x3 refer to Heavy Duty, Regular, and Extra Duty balls (in gross). The LINDO solution is on the following page. a) How many balls of each type will Matchpoint product? b) Which constraints are limiting and which are not? Explain. c) How much would you be willing to pay for an extra man-hour of testing capacity? For how many additional man-hours of testing capacity is this marginal value valid? Why? d) By how much would the profit contribution of Regular balls have to increase to make it profitable for Matchpoint to start producing Regular balls? e) By how much would the profit contribution of Heavy Duty balls have to decrease before Matchpoint would find it profitable to change its production plan? f) 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.