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Problem 1-Managing Constraints: Scrub-a-dub-dub Company produces soaps a variety of soaps for personal care. All the soaps are known for their great quality. Because of the generous amount of shea butter in the 3 bestselling soaps, they are very hydrating and one of them even has wound healing properties. They all smell delicious are sought by people of all ages. To produce a batch of 100 soaps, the company incurs the following costs: $130 $81 18 $110 $62 15 Sales price Variable cost Fixed cost Total cost Gross profit $130 $88 20 108 $22 1.5 $31 $33 Pounds of Shea Butter Required: a. Assuming no raw material constraints and unlimited demand for soaps, what type of soap would maximize the company's contribution margin? Why? b. Assume that based on typical customer demand, Scrub-a-dub-dub will sell 12,000 batches of exfoliating soaps, 8,000 batches of medicated soaps, and 10,000 batched of transparent soaps. What will the firm's contribution margin be? The company's supplier of shea butter and coconut oil has announced a shortage of shea butter. Due to this inconvenience, Scrub-a-dub-dub will only be able to purchase 50,000 lbs of shea butter. How many batches of each soap should the company produce? What will the firm's contribution margin be? c. d. If the company uses shea b utter in other products, will the allocation you recommend in part (c) change? Why or why not