Product network of a given factory is shown in Figure $1.$ Note that weekly demand, unit

selling price, raw material cost, and unit operation time on machines A$,$ B$,$ and C are all

given in the figure. Weekly capacity of machines is $40$ hours.

A

B

A

C

Product N

$$110/$unit

$100$ units$/$week

RM$2$

$$20/$unit

Product M

$$100/$unit

$90$ units$/$week

RM$1$

$$40/$unit

$15$ min

$5$ min

$10$ min

$10$ min

a$)$ Analyze this network and decide what weekly production plan $($product mix$)$ should be in

order to maximize profit. What is the constraint in this system?

b$)$ The described system is modified in such way that machine B can work only $4$ days per

week $(32$ hours$)$ due to necessary repair. What is the optimal production plan $($product

mix$)$ in this case? What is the constraint?

c$)$ The marketing department in the original system expanded the new market, which

allowed the selling price for product M to be $$120/$unit$.$ What is the optimal production

plan for this case?