Solve the following LP problem graphically:
Maximize $z = 30x_1 + 10x_2$
subject to:
$$3x_1 + x_2 \leq 300$$
$$x_1 + x_2 \leq 200$$
$$x_1 \leq 100$$
$$x_2 \geq 50$$
$$x_1 - x_2 \geq 0$$
$$x_1, x_2 \geq 0$$

Find an initial solution and total cost of the transportation problem in Table 5(b) by using North-west corner method and Vogel's method.

Table 5(b)

A manufacturing firm produces two products. Each product must go through an assembly process and a finishing process. The product is then transferred to the warehouse, which has space for only a limited number of items. The following linear programming model has been developed for determining the quantity of each product to produce in order to maximize profit:

$$
\text{Maximize } Z = 30x_1 + 70x_2 \text{ (profit, $)}
$$
$$\text{Subject to } 4x_1 + 10x_2 \leq 80 \text{ (assembly, hours)}$$
$$14x_1 + 8x_2 \leq 112 \text{ (finishing, hours)}$$
$$x_1 + x_2 \leq 10 \text{ (inventory, hours)}$$
$$x_1, x_2 \geq 0$$

Solve the problem graphically

Consider the information of the following table:

(i) Draw the appropriate network, (ii) Calculate ET and LT of each activity, (iii) Find the critical path, and (iv) Calculate FF for each activity

The ELECTROCOMP corporation manufactures two electrical products: air conditioners and large fans. The assembly process is similar in requiring certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan may be sold for a$15 profit. Formulate and solve this LP production mix situation, and find the best combination of air conditioners and fans that yields the higher profit.

Find an initial solution and total cost of the transportation problem in Table 5(b)
(i) by using Vogel's method, (ii) by lowest cost method

Table 5(b)

What is ergonomics? Why is ergonomics important?

"Steam power plants are located beside the river". Do you think the location is appropriate? Justify your answer.

Write down the effect of bad layout in any industry.

Consider the following linear programming formation:
$$minimize \ cost =$1X_1 + $2X_2$$
Subject to:
$$X_1 + 3X_2 \geq 90$$
$$8X_1 + 2X_2 \geq 160$$
$$3X_1 + 2X_2 \geq 120$$
$$X_2 \leq 70$$
What is the optimum solution?

Distinguish between Re-engineering and Reverse Engineering with example.

Explain the meaning and significance of plant location. How will you decide the location of a mini steel plant in Sirajgonj?

Circumstances dictate that a processor of dairy foods determine for a given day what his output of two different products will be. The following are the existing constraints:
$$X \ge 0 \ Y \ge 0 \ 2X + 8Y \ge 80 \ 4X + 2Y \ge 56 \ 3X + 3Y \ge 75$$
and the objective function, which is to be minimized, is as follows: $$C =$30X + $10Y$$ (X, Y = hundreds of pounds to be processed)

PM computer service assembles customized personal computers from generic parts. Formed and operated by part-time UMass Lowell students Paullette Tyler and Maureen Becker, the company has steady growth since it started. The company assembles computers mostly at night, using part time students. Paullette and Maureen purchase generic computer parts in volume at a discount from a variety of sources whenever they see a good deal. Thus, they need a good forecast of demand for their computers so that they will know how many parts to purchase and stock. They have compiled demand data for the last 12 months as reported below:

Forecast the demand for January (period 13)

• Using 3-month moving average.
• Using exponential smoothing with smoothing parameter $\alpha = 0.3$ (forecast value for period 1 is 37).

Find out the possible profit of the following LP model by solving graphically if-
Objective function $z = 6x_1 + 8x_2$
Subjected to $x_1 + 2x_2 \le 12$
$2x_1 + x_2 \le 20, x_1 \ge 0, x_2 \ge 0$