An order is placed to a firm for 25 diecast parts made from metals. Each part wi

Question

An order is placed to a firm for 25 diecast parts made from metals. Each part will be sold for $4500. The production cost for an individual part will cost $2000. At the end of an inspection, a part can be classified as good with 0.80 probability. Parts that classified as good but are not sold can be recycled at a value of $750. Parts that do not meet the inspection have a unit salvage value of $150. Firm has to pay $400 per unit short to the customer if the demand is not fully met. In addition, if the number that can be delivered is less than 23, there is an additional fixed penalty of $11,000 (i.e. if 20 parts can be delivered, the total penalty is (25-20)600 + 11,000=$14,000).

a. Find the expected profit for the given production quantity.

b. What is the production quantity that maximizes the expected profit?

c. Find the probability of losing money when the order quantity in part b. is used.

d. Assume that there is a process improvement that can improve production quality. If this improvement takes place, the probability of a given part meeting final inspection will raise to 95%. What is the maximum amount that should be paid for such an improvement?

e. Find the variance of the profit when the production quantity in part b is used.

Explanation / Answer

Residential and commercial space-cooling demands are increasing steadily throughout the world as what once was considered a luxury is now seemingly a necessity. Air-conditioning manufacturers have played a big part in making units more affordable by increasing their efficiency and improving components and technology. The competitiveness of the industry has increased with demand, and there are many companies providing air conditioning units and systems.

Air conditioning systems vary considerably in size and derive their energy from many different sources. Popularity of residential air conditioners has increased dramatically with the advent of central air, a strategy that utilizes the ducting in a home for both heating and cooling. Commercial air conditioners, almost mandatory in new construction, have changed a lot in the past few years as energy costs rise and power sources change and improve. The use of natural gas-powered industrial chillers has grown considerably, and they are used for commercial air conditioning in many applications.

Two air conditioners may look entirely dissimilar in both size, shape, and configuration, yet both function in basically the same way. This is due to the wide variety of applications and energy sources available. Most air conditioners derive their power from an electrically-driven motor and pump combination to circulate the refrigerant fluid. Some natural gas-driven chillers couple the pump with a gas engine in order to give off significantly more torque.

As the working fluid or refrigerant circulates through the air-conditioning system at high pressure via the pump, it will enter an evaporator where it changes into a gas state, taking heat from the opposing fluid medium and operating just like a heat exchanger. The working fluid then moves to the condenser, where it gives off heat to the atmosphere by condensing back into a liquid. After passing through an expansion valve, the working fluid returns to a low pressure

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