An engineering firm would like to increase its return on five potential new engineering and development$$ projects, as shown in the accompanying project information and$$ model, but the project manager knows that this will require more cash$$ and$/$or personnel. Conduct a$$ what$-$if analysis of the optimal solution as the cash limitation varies from$$ $$150,000$ to$$ $$230,000$ in increments of$$ $$20,000,$ and the personnel limitation varies from $12$ to $16.$ Summarize the returns for these solutions in the form of a heat map. Identify the solutions that represent the lowest amount of resources required to achieve each distinct return value.

Choose the heat map that correctly summarizes the returns for each solution.

Click here to view heat map b$.$ LOADING...

Click here to view heat map d$.$ LOADING...

Click here to view heat map c$.$ LOADING...

Click here to view heat map a$.$ LOADING...

Part $2$

Identify the solutions that represent the lowest amount of resources required to achieve each distinct return value. Complete the table below.

Personnel

Cash Requirement

Lowest Return

enter your response here

$$$enter your response here

Second Lowest Return

enter your response here

$$$enter your response here

Third Highest Return

enter your response here

$$$enter your response here

Second Highest Return

enter your response here

$$$enter your response here

Highest Return

enter your response here

$$$enter your response here

Part $3$

Which of the following best describes the best options and$$ trade$-$offs that must be made to increase the$$ returns?

A$.$

In order to achieve a greater$$ return, it is sometimes necessary to increase the cash requirement.$$ However, to achieve the greatest$$ return, only the personnel requirement needs to be increased.

B$.$

In order to achieve a greater$$ return, it is sometimes necessary to increase the cash requirement.$$ However, to achieve the greatest return commareturn, it is also necessary to increase the personnel requirement.

C$.$

In order to achieve a greater$$ return, it is always necessary to increase the personnel requirement.$$ However, to achieve the greatest return commareturn, it is also necessary to increase the cash requirement.

D$.$

In order to achieve a greater$$ return, it is sometimes necessary to increase the personnel requirement.$$ However, to achieve the greatest$$ return, only the cash requirement needs to be increased.