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 $4$ hours of assembly, $3$ hours of finishing, and $1$ hour of inspection. Each chair requires $3$ hours of assembly, $2$ hours of finishing, and $2$ hours of inspection. The selling price per table is $$140$ while the selling price per chair is $$90.$ Currently, each week there are $220$ hours of assembly time available, $160$ hours of finishing time, and $45$ hours of inspection time. Assume that one hour of assembly time costs $$5\mathrm{.}00$; one hour of finishing time costs $$6\mathrm{.}00$; one hour of inspection time costs $$4\mathrm{.}50$; 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 it was decided that all the labor hour costs have to be covered through the sale of the tables and chairs, regardless of whether or not all the labor hours are actually used. How would the objective function be written?

Select one:

a$.$

Maximize $140$T $+90$C

b$.$

Minimize $140$T $+90$C

c$.$

Maximize $97\mathrm{.}5$T $+54$C

d$.$

Maximize T $+$ C