Question $5$ options:

$30.$ Production Routing Lurix Electronics manufactures two products which can be produced on two different production lines. Both products have their lowest production costs when produced on the more modern of the two production lines. However, the modern production line does not have the capacity to handle the total production. As a result, some production will have to be routed to an older production line. Shown below are the data for total production requirements, production line capacities, and production costs:

Production Cost$/$Unit

Modern Line

Old Line

Minimum Production Requirements

Product $1$

$$3\mathrm{.}00$

$$5\mathrm{.}00$

$500$ units

Product $2$

$$2\mathrm{.}50$

$$4\mathrm{.}00$

$700$ units

Production Line Capacities

$800$

$600$

Formulate a linear programming model that can be used to make the production routing decision, with the goal of minimizing cost. What is the recommended decision and the total cost?

X$1,1=$ Number of Units of Product $1$ Produced on the Modern Line $=$

X$1,2=$ Number of Units of Product $1$ Produced on the Old Line $=$

X$2,1=$ Number of Units of Product $2$ Produced on the Modern Line $=$

X$2,1=$ Number of Units of Product $2$ Produced on the Old Line $=$

Cost $=$

$($Format xxxx$)$ Hint: Cost is between $3800$ and $3900$