A new small manufacturing company, IGEW, makes two customized computer models, the CFH Model and the XPQ Model. It is a family-run business that is not operating on a production line where many units can be made each day. IGEW firmly believes that these two products, created one at a time with specially designed machinery, will lure Generation Z* eventually into its fold, although no statistical evidence has been gathered yet to support this projection.

Considering the requisite data and formulating the problem as a linear program (LP), IGEW has developed the following program for each day.

Maximize Z=1_X1 + 5_X2 (profit in thousands)

s.t.

_5X1 + 4_X2 68 (available assembly hours)

4_X1+12_X2 64 (available labor hours)

9_X1 + _5X2 45 (minimal production level)

_X1, _X20

where is the number of basic CFH Models and is the number of XPQ models designated for production during the next timeframe.

1. Graph the constraints in the space below or on the next page and use the graphical method (not the corner point method) to find the optimal solution to the LP. Indicate clearly the feasible region. Recall that the optimal solution consists of the optimum and the maximum value. At least one iso-profit or iso-cost line must be drawn. Label the equation of at least one of them on the line itself. A non-integer solution, if one exists, should be expressed in hundredths.
2. How many CFH Models and XPQ Models can be produced daily? What is the best profit IGEW can realize?
3. Which constraints are binding at the optimal solution? Specify the slack or surplus for all resources. Use a Resource Utilization Table to display the results.

4. At the optimal solution, how many assembly hours should be used? How many labor hours? By how much is the required production level surpassed, if at all?