linear programming

[janet]

The cost to run machine 1 for an hour is $2. during that hour , machine 1 produces 240 bolts and 100 nuts. The cost to run machine 2 for an hour is $2.40. During that hour machine 2 produces 160 bolts and 160 nuts. With a combined running time of no more than 30 hours, how long each machine run to produce an order of at least 2080 bolts and 1520 nuts at the minimum operating cost?

 

[galactus]

Let x=number of hours to run machine 1 and let y=number of hours to run machine 2.

Now, try setting up the inequalities.

You are minimizing cost. So, the objective function will involve cost. What is the cost of running machines 1 and 2 for x and y hours?.

The total operating time can be NO MORE than 30.

\(\displaystyle x+y\leq 30\)

Construct two more inequalities for the number of nuts and bolts.

Assume \(\displaystyle x, y \geq 0\).


Let me know what you come up with.

Do you know how to use Excel Solver?. It does a fine job of solving these problems.