PROBLEM $1$

a$)$ Decision Variables

M $=$ Number of units sold through Marine

B $=$ Number of units sold through Business

R $=$ Number of units sold through Retail

D $=$ Number of units sold through Direct

b$)$ Objective function: Max Z $=95$M $+98$B $+82$R $+77$D

c$)$ Constraints:

$1.$ Advertising budget limit: $13$M $+14$B $+10$R $+13$D $<=15000$

$2.$ Salesforce hours availability: $2$M $+3$B $+3$R $+1$D $<=2700$

$3.$ Total production level: M $+$ B $+$ R $+$ D $=1000$

$4.$ Retail store requirement: R $>=150$

$5.$ Non$-$negativity: M $>=0$; B $>=0$; R $>=0$; D $>=0$

a$)$ What is the optimal solution to Electronic Communication$$s problem? Explain what it means.

b$)$ What is the objective value? Explain the meaning of the objective value.

c$)$ Out of the $4$ main constraints listed in Problem $1,$ which one$($s$)$ are binding? Use c$1,$ c$2,$ etc. in your answers, and mention why each one is binding or not.

d$)$ Interpret the value of the shadow price corresponding to the salesforce hours availability constraint $($i$.$e$.,$ constraint c$2).$

e$)$ Interpret the lower and upper ranges of the objective coefficient corresponding to your Marine decision variable.

f$)$ Now assume the new unit profit value for M goes up to $$100$ per unit $($from the current amount of $$95).$ Is that going to change the optimal solution to the problem? Why?