Hi, Sir.

I want to know this problem.

This problem is number 9 of chapter 13 in Business Analytisc 2ed.

For the Valencia Products model in Problem 1, graph the constraints and identify the feasible region. Then identity each of the comer points and show how’ increasing the objective function value identifies the optimal solution. 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. a. Identify the decision variables, objective function, and constraints in simple verbal statements. b. Mathematically formulate a linear optimization model.

## Expert Answer

**a.**

Let x= number of Laserstop

y= number of SpeedBuster

**x and y are decision variables.**

For x number of Laserstop, A required is 18x and B required is 6x

For y number of Speedbuster, A required is 12y and B required is 10y

But the number of As and Bs are limited (A is 4000 and B is 3500)

Hence, **constraints are: 18x+12y <= 4000**

**6x+10y <= 3500**

And our objective is to maximise profit. Profit is given by $(24x+40y).

So the **objectove function is Maximise 24x+40y**.

**b.**

Linear optimization model is combination of objective functions and constrains, which in this case is:

**Maximise 24x+40y**

**Subject to:**

**18x+12y <= 4000**

**6x+10y <= 3500**

** x,y <=0**