Question $6$

A company assembles and packages clocks. The basic model requires $30$ minutes to assemble and $20$ minutes to package, while the fancy model requires one hour to assemble and $30$ minutes to package. There are $30$ hours available per week to assemble the clocks, and $12$ hours per week available to package the clocks. Each basic clock yields a $$2\mathrm{.}50$ profit, and each fancy clock yields a $$4$ profit. Using the following decision variables:

B: weekly number of basic clocks to assemble$$

F: weekly number of fancy clocks to assemble $$

what is the company's profit optimization problem?$$

A$.$

max $2\mathrm{.}5$B $+4$F subject to: $0\mathrm{.}5$B $+$ F $<=30$; $0\mathrm{.}33$B $+0\mathrm{.}5$F $<=12$; B$,$ F $>=0$; B$,$ F are integers

B$.$

min $0\mathrm{.}5$B $+$ F subject to: $2\mathrm{.}5$B $+4$F $<=30$; $0\mathrm{.}33$B $+0\mathrm{.}5$F $<=12$; B$,$ F $>=0$; B$,$ F are integers

C$.$

min $0\mathrm{.}5$B $+$ F subject to: $2\mathrm{.}5$B $+4$F $<=30$; $0\mathrm{.}33$B $+0\mathrm{.}5$F $<=12$; B$,$ F $>=0$

D$.$

max $2\mathrm{.}5$B $+4$F subject to: $0\mathrm{.}5$B $+$ F $<=30$; $0\mathrm{.}33$B $+0\mathrm{.}5$F $<=12$; B$,$ F $>=0$