# Question & Answer: Sox Engineering designs and constructs air conditioning and heating​ (HVAC) systems…..

Sox Engineering designs and constructs air conditioning and heating​ (HVAC) systems for hospitals and clinics. Currently the​ company’s staff is overloaded with design work. There is a major design project due in 9 weeks. The penalty for completing the design late is ​\$14,000 per​ week, since any delay will cause the facility to open later than​ anticipated, and cost the client significant revenue. If the company uses its inside engineers to complete the​ design, it will have to pay them overtime for all work. Sox has estimated that it will cost ​\$10,000 per week​ (wages and​ overhead), including late​ weeks, to have company engineers complete the design. Sox is also considering having an outside engineering firm do the design. A bid of ​\$85,000 has been received for the completed design. Yet another option for completing the design is to conduct a joint design by having a third engineering company complete all electromechanical components of the design at a cost of ​\$52,000. Sox would then complete the rest of the design and control systems at an estimated cost of ​\$30,000. Sox has estimated the following probabilities of completing the project within various time frames when using each of the three options. Those estimates are shown in the following​ table:

 Probability of Completing the Design Option On Time One Week Late Two Weeks Late Three Weeks Late Internal Engineers 0.4 0.5 0.1 — External Engineers 0.2 0.5 0.2 0.1 Joint Design 0.2 0.2 0.4 0.2

The expected monetary value using inside engineers to complete the design is ​\$______​(Enter your response as an integer.​)

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The expected monetary value using outside engineers to complete the design is ​\$______​(Enter your response as an integer.​)

The expected monetary value of conducting a joint design is ​\$______​(Enter your response as an integer.​)

## Expert Answer

Internal Engineers Option:

Wages per week = \$10,000

Late Penalty cost = \$14,000 beyond 9 weeks

For Internal Engineers the payoff or cost for the project as per week schedule is as follows:

 Events Cost Structure Payoff Probability of completion Expected Payoff On time (in 9 weeks) Wages and OH for 9 days 9 x 10,000 = 90,000 0.4 (0.4)(90,000) = 36,000 One week late (in 10 weeks) Wages and OH for 10 days + penalty for 1 week delay (10)(10,000) + (1)(14,000) = 114,000 0.5 (0.5)(114,000) = 57,000 Two weeks late (in 11 weeks) Wages and OH for 11 days + penalty for 2 week delay (11)(10,000) + (2)(14,000) = 138,000 0.1 (0.1)(138,000) = 13,800 Three weeks late (in 12 weeks) Wages and OH for 12 days + penalty for 3 week delay (12)(10,000) + (3)(14,000) = 162,000 0 (0)(139,000) = 0 Expected Monetary Value 106,800

EMV using Inside Engineers to complete design = \$106,800

External Engineers Option:

Bid Cost = \$85,000

Late Penalty cost = \$14,000 beyond 9 weeks

For Internal Engineers the payoff or cost for the project as per week schedule is as follows:

 Events Cost Structure Payoff Probability of completion Expected Payoff On time (in 9 weeks) Bid Cost 85,000 0.2 (0.2)(85,000) = 17,000 One week late (in 10 weeks) Bid Cost + penalty for 1 week delay 85,000 + (1)(14,000) = 99,000 0.5 (0.5)(99,000) = 49,500 Two weeks late (in 11 weeks) Bid Cost + penalty for 2 week delay 85,000 + (2)(14,000) = 113,000 0.2 (0.2)(113,000) = 22,600 Three weeks late (in 12 weeks) Bid Cost + penalty for 3 week delay 85,000 + (3)(14,000) = 127,000 0.1 (0.1)(127,000) = 12,700 Expected Monetary Value 101,800

EMV using External Engineers to complete design = \$101,800

Joint Design Option:

Total Cost of project = \$52,000 + \$30,000 = \$82,000

Late Penalty cost = \$14,000 beyond 9 weeks

For Internal Engineers the payoff or cost for the project as per week schedule is as follows:

 Events Cost Structure Payoff Probability of completion Expected Payoff On time (in 9 weeks) Total Joint Cost 82,000 0.2 (0.2)(82,000) = 16,400 One week late (in 10 weeks) Total Joint Cost + penalty for 1 week delay 82,000 + (1)(14,000) = 96,000 0.2 (0.2)(96,000) = 19,200 Two weeks late (in 11 weeks) Total Joint Cost + penalty for 2 week delay 82,000 + (2)(14,000) = 110,000 0.4 (0.4)(110,000) = 44,000 Three weeks late (in 12 weeks) Total Joint Cost + penalty for 3 week delay 82,000 + (3)(14,000) = 124,000 0.2 (0.2)(124,000) = 24,800 Expected Monetary Value 104,400

EMV using Joint Design option to complete design = \$104,400