Question

A company producing a standard line and a deluxe line of dishwashers has the following time requirements (in minutes) in departments where either model can be processed.

STANDARD DELUXE
STAMPING 3 6
Motor installation 10 10
Wiring 10 15

The standard models contribute $20 each and the deluxe $30 each to profits. Because the Company produces other items that share resources used to make the dishwashers, the Stamping machine is available only 30 minutes per hour, on average. The motor installation Production line has 60 minutes available each hour. There are two lines for wiring, so the time Availability is 90 minutes per hour. Let x = number of standard dishwashers produced per hour y = number of deluxe dishwashers produced per hour.

Required:
a. Write the formulation for this linear program and then solve.
b. What is the value of the optimal profit ?

Answer 1

Complete Question

Complete Question is attached below

Answer:

$M=160$

Step-by-step explanation:

From the question we are told that:

Standard models contribute $20

Deluxe  models contribute $30

Availability Average :

Stamping machine S= 30 minutes per hour

Motor installation Production M=60 minutes

Wiring is W=90 minutes per hour

Generally the formulation of the linear program is given as

$Maximium (M)=20x + 30 y$

Where

For Stamping machine

$S= 3x + 6y \leq 30.....Equ 1$

For Motor installation Production

$10x + 10y \leq 60....Equ 2$

For Wiring

$10x + 15y \leq 90....Equ3$

Therefore

Solving Equ...(1,2,3) simultaneously we have

$x=2\\\\y=4$

Therefore

$Maximium\ (M)=20x + 30 y$

$M=20(2)+30(4)$

$M=160$