[Problem 3] Old Dominion Chemicals Inc. (Challenging problem)

Old Dominion Chemicals Inc. produces two products: formula Y and formula Z. Production of both products requires the same two processes. A unit of formula Y requires 3 hours on the first process and 4 hours on the second process. A unit of formula Z requires 5 hours on the first process and 2 hours on the second process. The maximum available production time for process one ins 60 hours, and for process two is 70 hours.

The production of formula Z results in a by-product, formula ZX. Some of formula ZX can be marketed at a profit. However, production of formula ZX in excess of 10 units is not desirable because there is no market beyond that level. The production process for formula Z yields 4 units of formula ZX for each unit of formula Z. Unit profits are $5 per unit of formula Y and $10 per unit of formula Z. The by-product, formula ZX, yields a profit of $3 per unit. If formula ZX cannot be sold, it should be destroyed at a cost of $2 per unit. The marketing department reports that the demand for formula Y and formula Z is unlimited. As given above, the demand for formula ZX is only 10 units.

Formulate a linear programming model that will determine the maximum total profit.