$($a$)$ Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products $1$ and $2.$

If required, round your answer to two decimal places.

Product $1$ Product $2$

Production

Select your answer $-$ hat$()$

What is the upper limit of what you would be willing to pay per hour of overtime in the department you recommended?

If required, round your answer to two decimal places.

quantities if overtime is made available. What are the optimal production quantities, and what is the revised total contribution to profit?

If required, round your answer to two decimal places.

Product $1$ Product $2$

Production

If required, round your answer to nearest whole number.

Total Profit

How much overtime do you recommend using in each department?

If required, round your answer to two decimal places. If you answer is zero, enter $"0".$

What is the increase in the total contribution to profit if overtime is used?

If required, round your answer to nearest whole number.