Sox Engineering designs and constructs air conditioning and heating systems for hospitals and clinics. Currently, the company's staff is overloaded with design work. There is a major design project due in $8$ weeks. The penalty for completing the design late is $$14,000$ per week because any delay will cause the facility to open later than anticipated and cost the client significant revenue. If the company uses its inside engineers to complete the design, it will have to pay them overtime for all work. Sox has estimated that it will cost $$12,000$ 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 $$90,000$ has been received for the completed design. Yet another option for completing the design is to conduct a joint design by having a third engineering company complete all electromechanical components of the design at a cost of $$50,000.$ 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 data table.

What is the best decision based on an expected monetary value $($EMV$)$ criterion?

Instructions:

Use the Yellow cells in creating your solution$/$answers to EMV questions.

Use formulas to demonstrate the source of your answers.

You may not need all the yellow cells provided.

Format your EMV answers to dollars.

Each correct answer is worth $3$ points. $($Total of $12$ Points$)$

Calculate the Expected Monetary Value for each option and

Select the best option in the dropdown on cell J$32.$

Probability of completing the design

$\backslash$table$[[$Option$,$On lime$,1$ Week Late,$2$ Weels Late,$3$ Weeks Late,$4$ Wee$],[$Internal$,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}1,,],[$External$,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}3,0\mathrm{.}1,],[$Joint$,0\mathrm{.}1,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}2,],[$Week $(s)$ Late $,1,2,3,],[,,,,,],[,,,,,],[,,,,,],[,,,,,],[,,,,,],[,,,,,],[,,,,,],[,,,,,],[,,,,,],[,,,,,],[,,,,,]]$