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3. Tucker Inc. produces high-quality suits and sport coats for men. Each suit requires 1.2 hours of cutting time and 0.7 hours of sewing time, use 6 yards of material, and provides a profit contribution of $190. Each sport coat requires 0.8 hours of cutting time and 0.6 hours of sewing time, use 4 yards of material, and provides a profit contribution of $150. For the coming week, 200 hours of cutting time, 180 hours of sewing time, and 1200 yards of fabric are available. Additional cutting and sewing time can be obtained by scheduling overtime for these operations. Each hour of overtime for the cutting operation increases the hourly cost by S15, and each hour of overtime for the sewing operation increases the hourly cost by $10. A maximum of 100 hours of overtime can be scheduled. Marketing requirements specify a minimum production of 100 suits and 75 sport coats. Let S = number of suits produced: SC = number of sport coats produced: D1 = hours of overtime for the cutting operation D2 = hours of overtime for the sewing operation a. What is the optimal solution, and what is the total profit? What is the plan for the use of overtime? b. A price increase for suits results in a profit contribution of $210 per suit. Would the optimal solution change? c. If the profit contribution per suit increases to $210 and overtime hourly cost for the cutting 2 operations increases to $30 from $15. Would the optimal solution change? d. Discuss the need for additional material during the coming week. If a rush order for material can be placed at the usual price plus an extra $8 per yard for handling, would you recommend the company consider placing a rush order for material? What is the maximum price Tucker would be willing to pay for an additional yard of material? How many additional yards of material should Tucker consider ordering? c. Suppose the minimum production requirement for suits is lowered to $75. Would this change help or hurt profit, and by how much