Valencia Products make automobile radar detectors and assembles two models: LaserStop and SpeedBuster. Both models use the same electronic components. 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, the profit per unit, and the resulting linear optimization model are given in the accompanying tables. Complete parts a through d$,$ answering each question independently relative to the original problem.

Click the icon to view the data table and linear optimization model.

a$.$ If the unit profit for SpeedBuster is decreased to $$132,$ how will the optimal solution and profit change?

The optimal solution when the profit for SpeedBuster is decreased to $$132$ is to produce LaserStop and SpeedBuster. This solution gives the possible profit, which is $$.$ This solution the same as the original solution, because the number of LaserStop models produced has and the number of SpeedBuster models produced as

$($Type integers or decimals rounded to two decimal places as needed.$)$

b$.$ If the unit profit for LaserStop is increased to $$225,$ how will the optimal solution and profit change?

The optimal solution when the profit for LaserStop is increased to $$225$ is to produce LaserStop and SpeedBuster. This solution gives the possible profit, which is $$,$ This solution the same as the original solution, because the number of LaserStop models produced has and the number of SpeedBuster models produced as

$($Type integers or decimals rounded to two decimal places as needed.$)$

c$.$ If an additional $2,500$ units of component A are available, can you predict how the optimal solution and profit will be affected?

If an additional $2,500$ units of component A are available, the profit will and the number of units produced will because

Component A a binding variable in the original problem.

d$.$ If a supplier delay results in only $3,000$ units of component B being available, can you predict how the optimal solution and profit will be affected? Can you explain the result?

If only $3,000$ units of component $B$ are available, the profit will and the number of units produced will because, in the original solution, Component B a binding variable and there were $3,000$ units used.L

Data Table and Linear Optimization Model

$\backslash$table$[[$Components Required$/$Unit$],[,$A$,$B$,$Profit$/$Unit$],[$LaserStop$,18,6,126],[$Speedbuster$,13,9,137]]$

After reviewing the components required and the profit for each model, the firm found the following linear optimization model for profit, where $L$ is the number of LaserStop models produced and $S$ is the number of SpeedBuster models produced.

Maximize Profit $=126L+137S$

$18L+13S4,000(ComponentA)$

$6L+9S3,500(ComponentB)$

$L0$ and $S0$