Question

Please ignore the numbers in the boxes with the red mark on it, I got them wrong. Please be kind and answer both!!!

Question 1:

Valencia Products makes automobile radar detectors and assembles two models: LaserStop and SpeedBuster. Both models use the same electronic components. 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. Implement the linear optimization model on a spreadsheet and use Solver to find an optimal solution. Interpret the optimal solution, identify the binding constraints, and verify the values of the slack variables. Maximize Profit = 124 L + 135 S 18 L + 13 S S 3000 5 L+8 SS 2500 L20 and S20 (Availability of component A) (Availability of component B)

Question 2:

Answer 1

1. for the system given we can draw the inequalities on a graph as

$18L+13S \leq 3000$

5L + 8S < 2500

0<S0 <1

so we get vertex point for the common region at

500 (0,230.769) 0 (166.667,0) --500

now giving this points to profit function ,

at (0,230.77) we get

$124L+135S=135(230.769)=31153.815$

at (166.67,0) we get

$124L+135S=124(166.67)=20667.08$

so the optimal solution is to produce 0 laserstop models and 230.77 speedbuster models .This solutions gives the maximum possible profit which is $31153.82

Since the optimal solution is (0,230.77) it lies on the line of component A so it is a binding constraint ,

for component B we get

$5L+8S+s=2500$

$s=2500-(8*230.77)=653.84$

Component A is a binding constraint and it has 0 slack

Component B is not a binding constraint and it has 653.85 slack

2. on graphing we get

we get vertex points at

100 (0,15.789) (30,0) 0 100 200 --100

(0,15.79) and (30,0) ,

giving this point to profit function

at (0,15.79)

$250(0)+340(15.789)=5368.6$

at (30,0)

$250(30)+0=7500$

so the optimal solution is to produce 30 standard desks and 0 deluxe desks , this solution gives the maximum possible profit which is $7500

availability of pine is not a binding constraint and it has slack

$70(30)+s=4000$

$\boldsymbol{s=1900}$

availability of oak is not a binding constraint and it has 800 slack

availability of labour is a binding constraint and it has 0 slack