Exercise 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 | 18 | 6 | $24 |
| SpeedBuster | 12 | 10 | $40 |
Identify the decision variables, objective function, and constraints in simple verbal statements.
Mathematically formulate a linear optimization model.
Step 1: Formulate the Linear programming Model
X1: LaserStop
X2: SpeedBuster
Maximize:
Z = 24X1 + 40X2
SUBJECT TO:
18X1 + 12X2 <= 4000
6X1 + 10x2 <= 3500
Step 2: Using lpSolve package of R to solve
library(lpSolve)
obj.fun <- c(24, 40)
constr <- matrix(c(18, 12, 6, 10), ncol = 2, byrow= TRUE)
constr.dir <- c("<=", "<=")
rhs <- c(4000, 3500)
prod.sol <- lp("max", obj.fun, constr, constr.dir, rhs, compute.sens = TRUE, all.int=TRUE)
prod.sol## Success: the objective function is 13320prod.sol$solution #decision variables values## [1] 0 333Conclusion: should not produce LaserStop & produce 333 SpeedBusters. Maximum is 13320.