Pierson Landscape Architects $($PLA$)$ develops and sells plans for various types of gardens and outdoor spaces. Customers buy the plans and then install the garden, the water feature, or other installation by themselves or by hiring a contractor who will take the plans and complete the job. The cost of producing one typical set of plans is

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Average Cost per Plan:$$Labor$,$ including architects and landscapers$ $537$Variable overhead, including supplies$213$Fixed production costs $($equipment and so on$)344$Fixed marketing and administrative costs$496$Total cost per set of plans$ $1,590$

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The fixed costs allocated to each plan are based on the assumption that the studio produces $2,500$ sets of plans annually.

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Required:

Treat each question independently. Unless stated otherwise, PLA charges $$2,000$ per set of plans.

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a$.$ How many sets of plans must the PLA produce annually to earn zero profits $($break even$)?$

b$.$ Market research estimates that a price increase to $$2,250$ per set of plans would decrease annual volume to $2,000$ sets of plans. The financial analyst at PLA estimates confirms that the variable cost per set of plans and the total fixed costs would remain unchanged if PLA produced and sold $2,000$ sets of plans at the new price. How would a price increase affect profits?

c$.$ PLA is currently operating at the normal volume of $2,500$ sets of plans annually. Blaine's Home Station, a chain of home and garden stores. has asked PLA for a set of $500$ plans exclusively for sale through Blaine's. Capacity at PLA is limited to $2,800$ sets of plans annually and because of the shortage of qualified individuals, PLA will not be able to increase capacity and provide the appropriate training in time to meet the extra demand. However, the plans for Blaine's could be produced at a total variable cost $($labor plus overhead$)$ of only $$600,$ because some of the plans would have common features. Blaine's has asked PLA for a special price of $$1,200,$ because of the size of the order and the reduced variable costs. Total fixed costs will be the same whether or not PLA accepts the special order. Would you suggest PLA accept the special order?

d$.$ Refer to the situation presented in requirement $($c$).$ PLA and Blaine's are still negotiating on price for the special order. What is the lowest price that PLA could charge and be no worse off for taking this order?

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