Table $8-4$

A small furniture manufacturer produces tables and chairs. Each product must go through

three stages of the manufacturing process: assembly, finishing, and inspection. Each table

requires $3$ hours of assembly, $4$ hours of finishing, and $2$ hours of inspection. Each chair

requires $2$ hours of assembly, $3$ hours of finishing, and $1$ hour of inspection. The selling price

per table is $$200$ while the selling price per chair is $$80.$ Currently, each week there are $300$

hours of assembly time available, $200$ hours of finishing time, and $50$ hours of inspection

time. Assume that one hour of assembly time costs $$10\mathrm{.}00$; one hour of finishing time costs

$$12\mathrm{.}00$; one hour of inspection time costs $$7$; and that whatever labor hours are not

required for the table and chairs can be applied to another product. Linear programming is

to be used to develop a production schedule. Define the variables as follows:

$T=$ number of tables produced each week

$C=$ number of chairs produced each week

Suppose that the problem described in Table $8-4$ is modified to specify that one$-$half of the

tables produced must have $8$ chairs, one$-$half must have $6$ chairs. How would this constraint

be written?

$C=14T$

$C=7T$

$C=3T$

$C=6T$