Recall the production model:

Max $10$x

s$.$t$.$

$5$x $<=40$

x $>=0$

Suppose the firm in this example considers a second product that has a unit profit of $$5$ and requires $2$ hours of labor time for each unit produced. Use y as the number of units of second product produced.

$($a$)$

Show the mathematical model when both products are considered simultaneously.

Max

s$.$t$.$

x $>=0,$ y $>=0$

$($b$)$

Identify the controllable and uncontrollable inputs for this model. $($Select all that apply.$)$

$($i$)$

controllable

x

y

labor hours

labor availability

unit profit

$($ii$)$

uncontrollable

x

y

labor hours

labor availability

unit profit

$($c$)$

Draw the flowchart of the input$-$output process for this model. $($Submit a file with a maximum size of $1$ MB$.)$

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$($d$)$

What are the optimal solution values of x and y$?($Let P be total profit in dollars.$)$

x $=$

y $=$

P $=$ $

$($e$)$

Is the model developed in part $($a$)$ a deterministic or a stochastic model? Explain.

The uncontrollable inputs are

$---$Select$---$

and

$---$Select$---$

$,$ so the model is

$---$Select$---$

$.$

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Micromedia offers computer training seminars on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting. Micromedia is currently planning a two$-$day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for the seminar is $$610$ per student. The cost for the conference room, instructor compensation, lab assistants, and promotion is $$9,520.$ Micromedia rents computers for its seminars at a cost of $$135$ per computer per day.

$($a$)$

Develop a model for the total cost $($C$)$ to put on the seminar. Let x represent the number of students who enroll in the seminar.

C $=$

$($b$)$

Develop a model for the total profit $($P$)$ if x students enroll in the seminar.

P $=$

$($c$)$

Micromedia has forecast an enrollment of $55$ students for the seminar. How much profit will be earned if their forecast is accurate?

P$(55)=$ $

$($d$)$

Compute the break$-$even point.

x $=$