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 these is limited to $5,000$ of component A and $4,500$ 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 solution the same as the original solution, because the number of LaserStop models produced has SpeedBuster. This solution gives the possible profit, which is $ and the number of SpeedBuster models produced as

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

$\backslash$table$[[$Components Required$/$Unit$],[,$A$,$B$,$Profit$/$Unit$],[$LaserStop$,19,5,126],[$Speedbuster$,13,8,137]]$

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 $=126L+137S$

$19L+13S5,000,($ Component $A)$

$5L+8S4,500$

$L0$ and $S0$