please help: skilled and unskilled labor to do a particular construction project

[ejing]

i am not a math major nor an engineering graduate but somehow our economics instructor asked this problem and i really don't know what to do.

2. The Miller Company uses skilled and unskilled labor to do a particular construction project. The cost of doing the project depends on the number of hours of skilled labor and the number of hours of unskilled labor that are used, the relationship being: C = 4 -3X1 – 4X2 + 2X12 + 3X22+ X1X2, where C is cost (in thousands of dollars) , X1 is the number of hours (in thousands) of skilled labor and X2 is the number of hours (in thousands) of unskilled labor.

a) Find the number of hours of skilled labor and the number of hours of unskilled labor that will minimize the cost of doing the project.
b) If the Miller Company has to purchase a license costing $2,000 to do this project (and if the cost of this license is not included in C), will this alter the answer to part a? If so, how will the answer change?

thank you for the help

 

[stapel]

i am not a math major nor an engineering graduate but somehow our economics instructor asked this problem and i really don't know what to do.

You posted this to "Differential Equations". Are you saying that your economics class is reviewing differential-equations techniques, that course being a prerequisite for your current class, but you haven't taken differential equations yet?

2. The Miller Company uses skilled and unskilled labor to do a particular construction project. The cost of doing the project depends on the number of hours of skilled labor and the number of hours of unskilled labor that are used, the relationship being: C = 4 -3X1 – 4X2 + 2X12 + 3X22+ X1X2, where C is cost (in thousands of dollars) , X1 is the number of hours (in thousands) of skilled labor and X2 is the number of hours (in thousands) of unskilled labor.

What are the definitions of x12 and x22? And are all of these variables subscripted, so they're really x₁, x₂, x₁₂, and x₂₂? What is the meaning of the subscripts? Are these meant to be partial derivatives or something?

a) Find the number of hours of skilled labor and the number of hours of unskilled labor that will minimize the cost of doing the project.

Finding the minimum value of C in terms of the four variables sounds like a calculus exercise. Have you not taken calculus, either?

b) If the Miller Company has to purchase a license costing $2,000 to do this project (and if the cost of this license is not included in C), will this alter the answer to part a? If so, how will the answer change?

This part is unclear. If the additional cost is not to be included in the cost considerations, then the cost considerations will not change. But the considerations ought to change, if the inputs change. Are they maybe asking for the cost relation to be updated to include the new cost, and then part (a) be re-done?

 

[ejing]

You posted this to "Differential Equations". Are you saying that your economics class is reviewing differential-equations techniques, that course being a prerequisite for your current class, but you haven't taken differential equations yet?


What are the definitions of x12 and x22? And are all of these variables subscripted, so they're really x₁, x₂, x₁₂, and x₂₂? What is the meaning of the subscripts? Are these meant to be partial derivatives or something?


Finding the minimum value of C in terms of the four variables sounds like a calculus exercise. Have you not taken calculus, either?


This part is unclear. If the additional cost is not to be included in the cost considerations, then the cost considerations will not change. But the considerations ought to change, if the inputs change. Are they maybe asking for the cost relation to be updated to include the new cost, and then part (a) be re-done?

I'm sorry. I don't really know which category to post this. I'm really dumb when it comes to math. numbers make my head spin.