GATE Mechanical Engineering

A company uses 3000 units of a part annually. The units are priced as given in the table below. It costs Rs. 150 to place an order. Carrying costs are 40 percent of the purchase pr...

Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, are $$ \begin{array}{|...

A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is __________hours (answer in integer)....

A set of jobs $U, V, W, X, Y, Z$ arrive at time $t = 0$ to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (...

A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a...

A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000 gears, the cost per or...

At the current basic feasible solution (bfs) $v_0 (v_0 \in \mathbb{R}^5)$, the simplex method yields the following form of a linear programming problem in standard form: minimize $...

In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each retailer...

In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is

Which one of the following is NOT a form of inventory?

Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be complete...

An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine...

An electric car manufacturer underestimated the January sales of car by 20 units, while the actual sales was 120 units. If the manufacturer uses exponential smoothing method with a...

The demand of a certain part is 1000 parts/year and its cost is Rs. 1000/part. The orders are placed based on the economic order quantity (EOQ). The cost of ordering is Rs. 100/ord...

Parts P1 - P7 are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time requi...

A project consists of five activities (A, B, C, D and E). The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediat...

A manufacturing unit produces two products Pl and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit ear...

Maximize $$\,\,\,\,\,\,\,\,\,Z = 5{x_1} + 3{x_2}$$ Subject to $$\,\,\,\,\,\,\,\,\,\,{x_1} + 2{x_2} \le 10,$$ $$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\...

Two models, $$P$$ and $$Q,$$ of a product earn profits of Rs. $$100$$ and Rs. $$80$$ per piece, respectively. Production times for $$P$$ and $$Q$$ are $$5$$ hours and $$3$$ hours,...

For a single server with Poisson arrival and exponential service time, the arrival rate is $$12$$ per hour. Which one of the following service rates will provide a steady state fin...

The standard deviation of linear dimensions $$P$$ and $$Q$$ are $$3\mu m$$ and $$4\mu m$$, respectively. When assembled, the standard deviation (in $$\mu m$$) of the following line...

In a single-channel queuing model, the customer arrival rate is $$12$$ per hour and the serving rate is $$24$$ per hour. The expected time that a customer is in queue is _______ mi...

The annual demand for an item is $$10,000$$ units. The unit cost is Rs. $$100$$ and inventory carrying charges are $$14.4\% $$ of the unit cost per annum. The cost of one procureme...

The demand for a two-wheeler was $$900$$ units and $$1030$$ units in April $$2015$$ and May $$2015,$$ respectively. The forecast for the month of April $$2015$$ was $$850$$ units....

Maximize $$\,\,\,\,Z = 15{x_1} + 20{x_2}$$ Subject to $$\eqalign{ & 12{x_1} + 4{x_2} \ge 36 \cr & 12{x_1} - 6{x_2} \le 24 \cr & \,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr} $$ The...

In $$PERT$$ chart, the activity time distribution is

For the linear programming problem: $$\eqalign{ & Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr & Subject\,\,to\,\,\,\, - 2{x_1} + 3{x_2} \le 9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...

In the notation $$(a/b/c) : (d/e/f)$$ for summarizing the characteristics of queuing situation, the letters $$‘b’$$ and $$‘d’$$ stand respectively for

Annual demand of a product is $$50,000$$ units and the ordering cost is Rs. $$7,000$$ per order. Considering the basic economic order quantity model, the economic order quantity is...

For a canteen, the actual demand for disposable cups was $$500$$ units in January and $$600$$ units in February. The forecast for the month of January was $$400$$ units. The foreca...

The annual requirement of rivets at a ship manufacturing company is $$2000$$ $$kg.$$ The rivets are supplied in units of 1 kg costing Rs. $$25$$ each. If it costs Rs. $$100$$ to pl...

A manufacturer has the following data regarding a product: Fixed cost per month $$=$$ Rs. $$50,000$$ Variable cost per unit $$=$$ Rs. $$200$$ Selling price per unit $$=$$ Rs. $$300...

The total number of decision variables in the objective function of an assignment problem of size $$n\,\, \times \,\,n$$ ($$n$$ jobs and $$n$$ machines) is

At a work station, $$5$$ jobs arrive every minute. The mean time spent on each job in the work station is $$1/8$$ minute. The mean steady state number of jobs in the system is ____...

A minimal spanning tree in network flow models involves

A manufacturer can produce $$12000$$ bearings per day. The manufacturer received an order of $$8000$$ bearings per day from a customer. The cost of holding a bearing in stock is Rs...

If there are $$m$$ sources and $$n$$ destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is

The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is

Consider an objective function $$Z\left( {{x_1},{x_2}} \right) = 3{x_1} + 9{x_2}$$ and the constraints $$\eqalign{ & {x_1} + {x_2} \le 8, \cr & {x_1} + 2{x_2} \le 4, \cr & {x_1} \g...

Jobs arrive at a facility at an average rate of $$5$$ in an $$8$$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facilit...

In exponential smoothening method, which one of the following is true?

A linear programming problem is shown below. $$\eqalign{ & Maximize\,\,\,\,3x + 7y \cr & Subject\,\,to\,\,\,3x + 7y \le 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4x...

In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

Customers arrive at a ticket counter at a rate of $$50$$ per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is $$1$$ $$min.$$...

Which one of the following is NOT a decision taken during the aggregate production planning stage?

One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One unit of product $${P_2}$$ requires $$2$$ $$kg$$ of resource $$...

Cars arrive at a service station according to Poisson's distribution with a mean rate of $$5$$ per hour. The service time per car is exponential with a mean of $$10$$ minutes. At s...

One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One unit of product $${P_2}$$ requires $$2$$ $$kg$$ of resource $$...

The word Kanban is most appropriately associated with

Simplex method of solving linear programming problem uses

Annual demand for window frames is $$10000.$$ Each frame costs Rs. $$200$$ and ordering cost is Rs. $$300$$ per order. Inventory holding cost is Rs. $$40$$ per frame per year. The...

The demand and forecast for February are $$12000$$ and $$10275,$$ respectively. Using single exponential smoothening method (smoothening coefficient $$= 0.25$$), forecast for the m...

Little’s law is relationship between

A company uses $$2555$$ units of an item annually. Delivery lead time is $$8$$ days. The recorder point (in number of units) to achieve optimum inventory is

Consider the following Linear Programming problem $$(LLP)$$ Maximize: $$Z = 3{x_1} + 2{x_2}$$ $$\,\,$$ Subject $$\,\,$$ to $$\eqalign{ & \,\,\,\,\,\,\,{x_1} \le 4 \cr & \,\,\,\,\,\...

The expected time $$\left( {{t_e}} \right)$$ of a $$PERT$$ activity in terms of optimistic time $$\left( {{t_0}} \right)$$, pessimistic $$\left( {{t_p}} \right)$$ and most likely t...

Which of the following forecasting methods takes a fraction of forecast error into account for the next period forecast?

In an $$M/M/1$$ queuing system, the number of arrivals in an interval of length $$T$$ is a Poisson random variable (i.e., the probability of there being $$n$$ arrivals in an interv...

Consider the Linear programme $$(LP)$$ Max $$4x$$ + $$6y$$ Subject to $$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,3x + 2y \le 6 \cr & \,\,\,\,\,\,\,\,\,\,\,2x + 3y \le 6 \cr & \,\,\,\,\,\,...

A moving average system is used for forecasting weekly demand. $${F_1}\left( t \right)$$ and $${F_2}\left( t \right)$$ are sequences of forecasts with parameters $${m_1}$$ and $${m...

Capacities of production of an item over $$3$$ consecutive months in regular time are $$100,$$ $$100$$ and $$80$$ and in overtime are $$20,$$ $$20$$ and $$40.$$ The demands over th...

The maximum level of inventory of item is $$100$$ and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a un...

In a machine shop, pins of $$15mm$$ diameter are produced at a rate of $$1000$$ per month and the same is consumed at a rate of $$500$$ per month. The production and consumption co...

The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter tak...

A company has two factories $${S_1},$$ $${S_2}$$ and two warehouses $${D_1},$$ $${D_2}$$ . the supplies from $${S_1}$$ and $${S_2}$$ are $$50$$ and $$40$$ units respectively. Wareh...

The sales of a product during the last four years were $$860, 880, 870$$ and $$890$$ units. The forecast for the fourth year was $$876$$ units. If the forecast for the fifth year,...

Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points of the feasible region are $$...

A project has six activities $$(A$$ to $$F)$$ with respective activity durations $$7,5,6,6,8,4$$ days. The network has three paths $$A-B,C-D$$ and $$E-F.$$ All the activities can b...

Consider a single server queuing model with Poisson arrivals $$\left( {\lambda = 4/hour} \right)$$ and exponential service $$\left( {\mu = 4/hour} \right)$$. The number in the syst...

Consider a linear programming problem with two variables and two constraints. The objective function is: Maximize $${x_1} + {x_2}.$$ The corner points of the feasible region are $$...

A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a ‘first come first served’ queue discipline. Breakdowns occur on an ave...

A company produces two types of toys: $$P$$ and $$Q.$$ Production time of $$Q$$ is twice that of $$P$$ and the company has a maximum of $$2000$$ time units per day. The supply of r...

A company has an annual demand of $$1000$$ units, ordering cost of Rs.$$100$$/order and carrying cost of Rs.$$100$$/unit –year. If the stock-out costs are estimated to be nearly Rs...

In $$PERT$$ analysis a critical activity has

For a product, the forecast and the actual sales for December $$2002$$ were $$25$$ and $$20$$ respectively. If the exponential smoothing constant $$(\alpha )$$ is taken as $$0.2,$$...

The sale of cycles in a shop in four consecutive months are given as $$70, 68, 82 95.$$ Exponentially smoothing average method with a smoothing factor of $$0.4$$ is used in forecas...

A manufacturer produces two types of products, $$1$$ and $$2,$$ at production levels of $${x_1}$$ and $${x_2}$$ respectively. The profit is given is$$2{x_1} + 5{x_2}.$$ The product...

Market demand for springs is $$8,00,000$$ per annum. A company purchases these springs in lots and sells them. The cost of making a purchase order is Rs.$$1,200.$$ The cost of stor...

A project consists of activities $$A$$ to $$M$$ shown in the net in the following figure with the duration of the activities marked in days. The project can be completed

Arrivals at a telephone booth are considered to be Poisson, with an average time of $$10$$ minutes between successive arrivals. The length of a phone call is distributed exponentia...