Question $3$

Carl's Medical Equipment Company manufactures hospital gurneys. Its' most popular model, Ultra, sells for $$5,000.$ It has variable costs of $$2,800$ and fixed costs of $$1,000$ per unit, based on an average production run of $5,000$ units. It normally has four production runs a year, with $$400,000$ in setup costs each time. Plant capacity can handle up to six runs a year for a total of $30,000$ beds.

A competitor is introducing a new hospital gurney, similar to Ultra that will sell for $$4,000.$

Management believes it must lower the price to compete. Marketing believes that the new price will increase sales by $25\%$ a year. The plant manager thinks that production can increase by $25\%$ with the same level of fixed costs. The company currently sells all the Ultra gurneys it can produce.

Required:

a$.$ What is the annual operating income from Ultra at the current price of $$5,000$ and normal production?

b$.$ What is the annual operating income from Ultra if the price is reduced to $$4,000$ and sales in units increase by $25\%?$

c$.$ What is the target cost per unit for the new price if target operating income is $20\%$ of sales?