Problem $1$: $($Page $450$ Problem $1)$

Valencia Products makes automobile radar detectors and assembles two models: LaserStop and

SpeedBuster. The firm can sell all it produces. Both models use the same electronic components.

Two of these can be obtained only from a single supplier. For the next month, the supply of these

is limited to $4,000$ of component A and $3,500$ of component B$.$ The number of each component

required for each product and the profit per unit are given in the table.

Components Required$/$Unit

A B Profit$/$unit

LaserStop $186$ $$24$

SpeedBuster $1210$ $$40$

$($a$)$ Identify the decision variables, objective function, and constraints in simple verbal

statements.

$($b$)$ Mathematically formulate a linear optimization model.

Problem $2$: $($Page $450$ Problem $5)$

Implement the linear optimization model that you developed for Valencia Products in Problem $1$

in Excel and use Solver to find an optimal solution. Interpret the Solver Answer report and

identify the binding constraints and verify the values of the slack variables by substituting the

optimal solution into the model constraints.

Problem $3$: $($Page $452$ Problem $16)$

The figure below shows the Solver sensitivity report for Valencia Products in Problem $1.$ Using

ONLY the information in the sensitivity report, answer the following questions.

$2$

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$$11$ Numbers Produced LaserStop $0-3624361$E$+30$

$C$$11$ Numbers Produced SpeedBuster $333\mathrm{.}33333330401$E$+3024$

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R$.$H$.$ Side Increase Decrease

$D$$14$ Component A Used $40003\mathrm{.}33333333340002004000$

$D$$15$ Component B Used $3333\mathrm{.}333333035001$E$+30166\mathrm{.}6666667$

$($a$)$ Explain why the reduced cost for SpeedBuster is $0.$

$($b$)$ If the unit profit for SpeedBuster is decreased to $$35,$ can you predict how the optimal

solution and profit will change?

$($c$)$ If the unit profit for LaserStop is increased to $$64,$ can you predict how the optimal

solution and profit will change?

$($d$)$ If an additional $500$ units of component A are available, can you predict how the optimal

solution and profit will be affected?

$($e$)$ If a supplier delay results in only $3,400$ units of component B available, can you predict

how the optimal solution and profit will be affected?

Problem $4($Page $450$ Problem $3)$

Burger Office Equipment produces two types of desks, standard and deluxe. Deluxe desks have

oak tops and more$-$expensive hardware and require additional time for finishing and polishing.

Standard desks require $70$ board feet of pine and $10$ hours of labor, whereas deluxe desks require

$60$ board feet of pine, $18$ square feet of oak, and $15$ hours of labor. For the next week, the

company has $5,000$ board feet of pine, $750$ square feet of oak, and $400$ hours of labor available.

Standard desks net a profit of $$225,$ and deluxe desks net a profit of $$320.$ All desks can be sold

to national chains such as Staples or Office Depot.

$($a$)$ Identify the decision variables, objective function, and constraints in simple verbal

statements.

$($b$)$ Mathematically formulate a linear optimization model.

$3$

Problem $5($Page $451$ Problem $7)$

Implement the linear optimization model that you developed for Burger Office Equipment in

Problem $3$ in Excel and use Solver to find an optimal solution. Interpret the Solver Answer report

and identify the binding constraints and verify the values of the slack variables by substituting

the optimal solution into the model constraints.