Production Engineering

Production Engineering

Practice Exam #1

Open book. Show all your work.

1. The Break E. Van Company has decided to bid on the manufacture of brake systems for use in the space shuttle landing gear system. These brakes are used on each of the orbiters and are replaced after each mission. The component material cost is $100 per unit. There is a fixed cost of $70,000 for specialized manufacturing and test equipment. The average hourly labor rate within the Company is $45 with a factory burden rate of .4. Because the company has been making assorted brake linings for years, it does not believe that there is a learning curve effect. Instead, each lining (unit) will require 20 hours of semi-skilled craftsman earning $45 per hour. NASA has agreed to the following unit price formula based upon the number of brake systems they purchased (x):

S = 2000 - .6 x

(a)What is the break-even point?

(b)How many should be produced and sold to NASA to maximize profit?

(c)NASA has agreed to purchase 400 brake systems from the Break E. Van Company. What is the total profit received by the company and what is the mark-up for each break system? Profits are what percent of the Company’s total production cost?

2. (a) Based upon the following two years of sales data, complete Holt’s model to estimate the quarterly sales for 2010. Use S0 = 215 and G0 = 10 as initial values and use = .2,  = .3 as smoothing constants.

Quarter / Sales
Winter 2008 / 221
Spring 2008 / 235
Summer 2008 / 240
Fall 2008 / 243
Winter 2009 / 255
Spring 2009 / 266
Summer 2009 / 279
Fall 2009 / 287

(b) Forecast the spring and summer 2010 sales if the actual sales in the winter were 295.

3. A manufacturer that produces a single product having a seasonal demand is faced with decisions about production levels, work-force size, and overtime during a planning horizon of 6 weeks. Capacity is determined by a work-force level that is presently 100 people, each working a 40-hour week. Overtime, up to 8 hours per person per week, is possible. Labor costs average $10 per hour resulting in an overtime rate of $15 per hour. It takes 6 worker-hours to produce a unit of product. Product costs, other than labor, are $100 per unit. The cost to carry a unit of inventory for one week is 80 cents. Costs to change the work force are based on an estimate of $400 to hire and train a worker and $250 to layoff a worker. Estimated demands are 650, 700, 800, 900, 800, and 700. The current inventory level is 50 units. Ending inventory is set at 60 units and at least 100 workers must be on the payroll the last week of the planning horizon. Shortages are permitted only during the first two weeks. Formulate a linear program to solve this problem. Be sure to define your variables!

4. The N. Ventory Company must decide whether to purchase or produce a critical part used in the manufacture of compressors found in the F100 jet engine. Relevant cost data are given in Table 1.

Parameter / High quality
Supplier / Discount
Supplier / Produce
In house
Unit cost / $220 / $205 / $210
Order & setup cost / $350 / $350 / $1900
Production rate / N/a / N/a / 8000 per year
Reject (scrap) rate / 0 / 4% / 2%
Lead-time / 10 weeks / 7 weeks / 22 weeks[1]

Table 1 Data

Demand is constant at 50 units a month. Annual holding cost is 5 percent of the unit cost. The total number of units purchased or produced (total demand) must be increased to allow for the rejects. No backorders are permitted since shortages result in a work stoppage. Determine the least-cost inventory policy by completing Table 2.

High quality
Supplier / Discount
Supplier / Produce
In house
Economic Order Quantity (Q)
Reorder point (R)
Purchase or production cost
Inventory cost (order/setup + holding cost)
Total Cost

Table 2 Solutions

5. The Nomore Space Company purchases wholesale, stores, and then sellsat retail four different products used by astronauts and space tourists. These four products are space helmets, space suits, space boots, and a deluxe pair of space gloves.

The following tabled data is relevant:

Unit Cost / Order Cost**
($/order) / Demand rate per year / Storage space (Sq. ft. / unit)
space suit / $5,000 / $160 / 1,000 / 7
gloves, one pair* / $1,000 / $100 / 5,000 / 1
boots, one pair* / $2,000 / $90 / 10,000 / 2
helmet / $3,000 / $210 / 8,000 / 3

*NASA’s policy has been to issue several pairs to each astronaut

** Items are special ordered with very precise specifications

The annual carrying cost is 12 percent of the unit cost and Nomore has only 500 square feet of floor space available.

(a)Determine the optimal order quantities for these items given there is only 500 square feet of storage space..

(b)Once the order quantities have been determined, warehouse floor space must then be partitioned into four distinct areas because of highly restrictive environmental conditions required for each item.

(c)What is the total inventory cost (holding cost + ordering cost)?

(d)What would be the savings per year if unlimited floor space was available?

6. A Manufacturing Company (AMC) makes up to n different products all of which must be assembled over the same production line. A single production run is made once year for each product. The following data has been collected by AMC’s production engineering staff:

Ri = revenue (selling price) generated from one unit of product i

Ci = variable (unit) manufacturing cost of product i

Fi = fixed cost to produce product i (in any quantity)

Ti = production line time to produce one unit of product i (inminutes)

Si = production line setup time in hours to configure the line for product i

Ri = number of units of raw material needed to produce one unit of product i

AMC has a total manufacturing budget of B dollars for the coming year. The production line is available for a total of H hours during the year which includes both assembly time and setup time. There is a total of M units of the raw material available this coming year that is used in the manufacture of all of AMC’s products. The objective is to maximum the total profit for the coming year.

Letting xi = the production lot size for product i, formulate a linear optimization problem to determine which products should be produced and in what quantities for the coming year. Define any additional variables or parameters used in your formulation.

7. The Notso Brite Company has experienced only an 85 percent learning curve effect in the production of its best selling item – The Product[2]. Demand for The Product, x, is a function of its selling price, S(x), where S(x) = 400 - .006x. Relevant cost data is given in Table 1.

Material Cost / Factory Burden
Rate / Labor Rate / Fixed Cost / Learning curve / Labor hours for 1st unit
$3.50 per unit / .7 / $60 / hr / $10,000 / 85% / 20

Table 1 Relevant Cost Data

Complete the following table:

Production level / Units produced / Unit selling price / Total Profit / Profit per unit sold
Breakeven point / $0 / $0
Current production / 10,000 units
Maximum total profit point

1

[1]The number of weeks required to obtain raw material for production results in the long lead-time.

[2] Management has surmised that the reason for this is due to a high employee turnover rate. The company offers minimum wage, no benefits, and a stressful working environment.