$$b$)$ The objective function for the LP model$=$

Part $3$

Minimize Z$=$

$ $7\mathrm{.}50$

Upper V Subscript Upper A $1$

plus$ $6\mathrm{.}25$

Upper V Subscript Upper A $2$

plus$ $6\mathrm{.}50$

Upper V Subscript Upper A $3$

plus

$($shipping cost to customer$$ A$)$

$ $6\mathrm{.}75$

Upper V Subscript Upper B $1$

plus$ $7\mathrm{.}00$

Upper V Subscript Upper B $2$

plus$ $8\mathrm{.}00$

Upper V Subscript Upper B $3$

$($shipping cost to customer$$ B$)$

Part $4$Part $5$Part $6$Part $7$Part $8$Part $9$

$$c$)$ Subject$$ to:

Upper V Subscript Upper A $1$ Baseline plus Upper V Subscript Upper A $2$ Baseline plus Upper V Subscript Upper A $3$ Baseline equals $650$

Customer$$ A$\text{'}$s demand

Upper V Subscript Upper B $1$ Baseline plus Upper V Subscript Upper B $2$ Baseline plus Upper V Subscript Upper B $3$ Baseline equals $800$

Customer$$ B$\text{'}$s demand

Upper V Subscript Upper A $1$ Baseline plus Upper V Subscript Upper B $1$ Baseline less than or equals $400$

Warehouse$1\text{'}$s supply

Upper V Subscript Upper A $2$ Baseline plus Upper V Subscript Upper B $2$ Baseline less than or equals $500$

Warehouse$2\text{'}$s supply

Upper V Subscript Upper A $3$ Baseline plus Upper V Subscript Upper B $3$ Baseline less than or equals $600$

Warehouse$3\text{'}$s supply

For all Upper V Subscript ijgreater than or equals$0$

non negativity condition

Part $10$

Using a software the linear programming problem was solved and the following sensitivity report was$$ obtained:

Adjustable Cells

Variable

Final Value

Reduced Cost

Objective Coefficient

Allowable Increase

Allowable Decrease

Upper V Subscript Upper A $1$

$0$

$1\mathrm{.}50$

$ $7\mathrm{.}50$

$1$E$+30$

$1\mathrm{.}50$

Upper V Subscript Upper A $2$

$100$

$0\mathrm{.}00$

$ $6\mathrm{.}25$

$0\mathrm{.}25$

$0\mathrm{.}75$

Upper V Subscript Upper A $3$

$550$

$0\mathrm{.}00$

$ $6\mathrm{.}50$

$0\mathrm{.}75$

$0\mathrm{.}25$

Upper V Subscript Upper B $1$

$400$

$0\mathrm{.}00$

$ $6\mathrm{.}75$

$0\mathrm{.}50$

$1$E$+30$

Upper V Subscript Upper B $2$

$400$

$0\mathrm{.}00$

$ $7\mathrm{.}00$

$0\mathrm{.}75$

$0\mathrm{.}50$

Upper V Subscript Upper B $3$

$0$

$0\mathrm{.}75$

$ $8\mathrm{.}00$

$1$E$+30$

$0\mathrm{.}75$

Constraints

Name

Final Value

Shadow Price

Constraint RH Side

Allowable Increase

Allowable Decrease

Upper C $1$

$650$

$6\mathrm{.}50$

$650$

$50$

$550$

Upper C $2$

$800$

$7\mathrm{.}25$

$800$

$50$

$400$

Upper C $3$

$400$

negative $0\mathrm{.}50$

$400$

$400$

$50$

Upper C $4$

$500$

negative $0\mathrm{.}25$

$500$

$550$

$50$

Upper C $5$

$550$

$0\mathrm{.}00$

$600$

$1$E$+30$

$50$

Part $11$

$$d$)$ Based on the information given in the sensitivity$$ reports, the number of constraints that are binding$=$

$$

$5($enter your response as an $$integer$).$