Chapter 4.1, Problem 45E

PRODUCTION SCHEDULING Custom Office Furniture is introducing a new line of executive desks made from a specially selected grade of walnut. Initially, three models—A, B, and C—are to be marketed. Each model A desk requires $1\frac{1}{4}\text{hr}$ for fabrication, $1\text{hr}$ for assembly, and $1\text{hr}$ for finishing; each model B desk requires $1\frac{1}{2}\text{hr}$ for fabrication. $1\text{hr}$ for assembly, and $1\text{hr}$ for finishing; each model C desk requires $1\frac{1}{2}\text{hr}$, $\frac{3}{4}\text{hr}$, and $\frac{1}{2}\text{hr}$ for fabrication, assembly, and finishing, respectively. The profit on each model A desk is $\$26$, the profit on each model B desk is $\$28$, and the profit on each model C desk is $\$24$. The total time available in the fabrication department, the assembly department, and the finishing department in the first month of production is $310\text{hr}$, $205\text{hr}$, and $190\text{hr}$, respectively. To maximize Custom's profit, how many desks of each model should be made in the month? What is the largest profit the company can realize? Are there any resources left over?