Guernsey Company manufactures a single product. Estimated unit demand, selling price per unit, and labour cost of this product appear in Exhibit A$.$

Each unit of the product requires $4$ units of raw material. Raw materials are difficult to source and must be purchased via a contract. The contract requires that each month Guernsey Company purchases the same quantity of raw materials. Each unit of the raw material costs $$2\mathrm{.}50.$

The raw material is unstable and must be stored in a special building. The maximum amount of month end inventory is $5,000$ units. Any month end inventory more than $5,000$ units must be scrapped to yield a net realizable value of SO$.$ The warehouse owner charges Guernsey Company $$1\mathrm{.}00$ for each unit in inventory at the start of each month. Raw material inventory is expected to be $5,000$ units at the start of January.

Fixed costs at Guernsey Company are $$200,000$ per year.

Required

$1.$ What monthly inventory purchases yield the highest income and what is what is that income?

$2.$ The raw material supplier has offered to deliver any quantity of material daily. What is the ceiling price per unit that Guernsey Company should be willing to pay for materials in this alternative?

$3.$ Return to the data you used to address Question $1.$ A customer has agreed to purchase $2,800$ units of the product each month. This customer demands exclusivity $-$ that is Guernsey Company cannot sell this product to any other customer. What is the floor price Guernsey Company should be willing to accept for this alternative?