he Carson Stapler Manufacturing Company forecasts a $5,000-$ unit demand for its Sure $-$ Hold model stapler during the next quarter. This stapler is assembled from three major components: one base, one cartridge, and one handle. Each of these three components must be processed in each of Carson $$ s three departments: Forming, Finishing, and Testing. Until now, Carson has manufactured all three components itself. However, the forecast of $5,000$ ?units is a new high in sales volume, and it is not clear that Carson will have sufficient production capacity to make all the components. The company is considering contracting with an external supplier to produce at least some of the components.

The production time requirements per unit at Carson are as follows:

?Time Required $($ hours $/$ unit $)$ ?Capacity Available

Department Base Cartridge Handle $($ hours $)$

Forming $0\mathrm{.}030\mathrm{.}020\mathrm{.}05400$

Finishing $0\mathrm{.}040\mathrm{.}020\mathrm{.}04400$

Testing $0\mathrm{.}020\mathrm{.}030\mathrm{.}01400$

After considering the firm $$ s variable labor, material, and overhead costs, the accounting department has determined the unit manufacturing cost for each component. These data, along with the purchase price quotations by the external supplier, are as follows:

Component Manufacturing

Cost at Carson Purchase Cost from

External Supplier

Base $ $0\mathrm{.}75$ ?$ $0\mathrm{.}95$

Cartridge $ $0\mathrm{.}40$ ?$ $0\mathrm{.}55$

Handle $ $1\mathrm{.}10$ ?$ $1\mathrm{.}40$

Carson must deliver $5,000$ ?units in the next quarter. There is no limit to the number of components Carson may purchase from the external supplier. Thus, Carson will have the assembly capacity to make $5,000$ ?units.

Carson wants to minimize the total costs, including the cost of manufacturing $($ in $-$ house at Carson $)$ ?and the cost of purchasing components from the external supplier.