Linear Programming equations ( Problem with unrestricted variables)

[01sovit]

JoCo manufactures three products as follows
product 1:: profit: $2 labor hrs req for a unit: 2 machine hrs req for a unit: 1
product 2:: profit: $5 labor hrs req for a unit: 1 machine hrs req for a unit: 1
product 3:: profit: $3 labor hrs req for a unit: 2 machine hrs req for a unit: 2

budgeted hrs:: labor: 65 and machine: 80.
Other constraints: the budgeted hrs can be exceeded but the additional cost will be $15 per hour of labor and $10 per hour of machine.
Formulate the problem as an LP and please explain in detail the part were the unrestricted variables are used.

 

[stapel]

JoCo manufactures three products as follows
product 1:: profit: $2 labor hrs req for a unit: 2 machine hrs req for a unit: 1
product 2:: profit: $5 labor hrs req for a unit: 1 machine hrs req for a unit: 1
product 3:: profit: $3 labor hrs req for a unit: 2 machine hrs req for a unit: 2

budgeted hrs:: labor: 65 and machine: 80.

Other constraints: the budgeted hrs can be exceeded but the additional cost will be $15 per hour of labor and $10 per hour of machine.
Formulate the problem as an LP and please explain in detail the part were the unrestricted variables are used.

Things seem to be stated in terms of hours and units. Likely, you are expected to minimize production costs or maximize production. (The exercise doesn't seem to say.)

Do you know if the differently-valued "labor hours" can run concurrently, or must they run successively (so one unit requires five hours, at three different costs)? Same question for the "machine hours".

What variables did you pick? For what do they stand? What expressions and equations have you generated thus far? Where are you getting stuck?

Please be complete. Thank you!