Consider the following sensitivity report:

Variable Cells

Final

Reduced

Objective

Allowable

Allowable

Cell

Name

Value

Cost

Coefficient

Increase

Decrease

$C$$5$

#

$2$

$0$

$70$

$10$

$40$

$D$$5$

#

$4$

$0$

$30$

$53$

$5$

Constraints

Final

Shadow

Constraint

Allowable

Allowable

Cell

Name

Value

Price

R$.$H$.$ Side

Increase

Decrease

$E$$9$

#

$900$

$32$

$900$

$200$

$300$

$E$$10$

#

$2400$

$2$

$2400$

$200$

$800$

$E$$11$

#

$660$

$0$

$700$

$630$

$40$

$E$$12$

#

$180$

$0$

$280$

$180$

$480$

$1)$ How many decision variables are in the problem? $(2$ point$)$

$2)$ How many constraints are in the problem? $(2$ point$)$

$3)$ Which constriants are binding constriants? Why? $(2$ point$)$

$4)$ What is the minimum value of the coefficient of the first variable in the objective function without changing the current solution? Show the details of your answer. $(2$ point$)$

$5)$ What is the value of the objective function of the current solution? Show the details of your answer. $(4$ points$)$

$6)$ The manager of the corporation wants to introduce a new product that consumes one unit of each resource. The selling price of the product would be $$35.$ Is producing this product profitable? Show the details of your answer. $(4$ points$)$