R$1.$ You have opened a bakery beside MacEwan University. You produce $4$ products: cakes, cookies, bread, and

pastries. Here, $1$ unit of cookie and pastry implies a dozen of each. Each product goes through four processes:

mixing, shaping$/$forming$,$ baking, and cooling$/$packaging$.$ The amount of each product demanded each day, and

the profit margin is as follows:

Demand and profit information for each of four products

Cookies Cake Pastry Bread

Demand $($units$/$day$)40203030$

Margin $($$$/$unit$)15351214$

Each unit of each product requires the following machine time $($in hours$).$

Cookie Cake Pastry Bread

Mixing $0\mathrm{.}250\mathrm{.}50\mathrm{.}30\mathrm{.}2$

Shaping$/$Forming $0\mathrm{.}30\mathrm{.}750\mathrm{.}50\mathrm{.}25$

Baking $0\mathrm{.}31\mathrm{.}000\mathrm{.}40\mathrm{.}5$

Cooling$/$packaging $0\mathrm{.}20\mathrm{.}50\mathrm{.}250\mathrm{.}3$

a$)$ Assume the daily process capacity of each process, given the constraints on labor and machines are: Mixing

$=36$ hours $(3$ mixing stations running $12$ hours per day$),$ Shaping $56$ hours $(7$ stations running $8$ hours per

day$),$ Baking $=50$ hours $(5$ ovens at $10$ hours per day$),$ and cooling $40$ hours $(4$ cooling stations running $10$

hours per day$).$ Is there the capacity to meet the entire demand for all four products? $($i$.$e$.,$ find the aggregate

workload for each product$).(6$ points$)$