Recall the following times $($in minutes$)$ required for the components on each machine.

Machine

Component Shaper Grinder

$164$

$245$

$342$

Also recall that the shaper is available for $125$ hours, the grinder is available for $115$ hours, no more than $200$ units of component $3$ can be sold, up to $800$ units of each of the other components can be sold, and the company already has orders for $600$ units of component $1$ that must be satisfied.

Finally, recall that in previous step we determined that the profit margin for component $1$ is $$7,$ the profit margin for component $2$ is $$8,$ and the profit margin for component $3$ is $$6.$

To solve for the recommended production quantities that will maximize contribution to profit we will use Solver in Excel. Watch the video to learn how to create and solve the linear programming model for this problem. Note that the data in the video is not the same as what is given for this problem, but the process remains the same. Make sure to select the sensitivity and answer reports before exiting Solver.

The maximum profit is $ and occurs with the following production quantities.

component $1$ units

component $2$ units

component $3$ units