Patsy, Inc., manufactures two products, X and Y. Each product must be processed in each of three departments: machining, assembling, and finishing. The hours needed to producé one unit per department and the maximum possible hours per department follow: 74)

Required:
a Given the objective and constraints, what is the most profitable number of units of X and units of Y to manufacture? Determine your answer by utilizing the graphic solution method.
b What would your answer be to part a if there were no restrictions on X and Y? Use the simplex algorithm method to obtain your answer.

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Machining Assembling Finishing PRODUCTION HOURS PER UNIT Product X Product Y 4 021 Maximum capacity, hours 420 2 500 2 3 600 722 Other restrictions follow: X=20 Y= 20 The objective is to maximize profits where profits = $4X + $2Y. "Problems marked with an asterisk are based on information in the Appendix of this chapter.