QUESTION THREE $[15$ MARKS$]$

A construction company in Muscat that is in the business of producing precast concrete products in its outdoor yard has just concluded a study with researchers at SQU regarding early performance of its products in exposed wet conditions. The company estimates that if he produces concrete blocks before the onset of anticipated rains at the beginning of the winter season, it will be able to sell up to a maximum of $3,000$ pallets of concrete blocks because of the demand that exists at that time of year. Given that the quality of the blocks will be of good quality, it is anticipated that it can sell at $$3$ per block. However, it believes that demand for concrete blocks will increase as construction is anticipated to peak after the month of heavy rains. The company anticipates the demand to increase by $360$ pallets for every month that he delays the sale of fabricated blocks past this wet winter month. However, the quality of the concrete blocks is anticipated to deteriorate from outdoor exposure to heavy rains and subsequent dry warmer weather. The price of product is anticipated to drop at a rate of $45$ cents per pallet per month. In addition, the company estimates approximately $50$ pallets per month will spoil for each month he delays picking as a result of deteriorated concrete blocks and rough material handling within its production yard.

Use the information provided to answer the following questions:

a$)$ From an Engineering Economics perspective, what type of problem is this?

$[3$ Marks$]$

b$)$ When is the best time for the construction company to sell their concrete block products to obtain the largest total cash return?

$[6$ Marks$]$

c$)$ How much will the company receive for their concrete blocks at that time?

$[6$ Marks$]$