6. (25 pts.) The Country Rose Truck Stop at the crossroads of Interstates 70 and 57 near Effingham, Illinois is a large full-service independent truck stop serving truckers with fuel, ample overnight parking, wireless internet access, showers, a game room with pool tables, and a 24/7 restaurant. The restaurant, one of the largest in the Midwest, serves a simple but wide menu including burgers, club and Reuben sandwiches, catfish, and \"breakfast anytime\". Scheduling wait staff in the restaurant has long been a challenge due to the hour-by-hour change in restaurant traffic. Mae Allen, the owner-manager of the truck stop's restaurant, has looked at her typical customer traffic over a 24-hour period. Reviewing traffic in one-hour increments Mae came up with the table below showing how many persons should generally be scheduled to wait tables through the day. Hou Staff r 00:0 6 0 01:0 4 0 02:0 3 0 03:0 2 0 04:0 3 0 05:0 5 0 06:0 14 0 07:0 17 0 08:0 20 0 09:0 15 0 10:0 10 0 11:00 15 Hour Staff 12:00 25 13:00 20 14:00 12 15:00 8 16:00 8 17:00 15 18:00 23 Mae could employ both full- and part-time staffers. Fulltimers work 8 hour shifts and part-timers work shifts of 19:00 19 anything under 8 hours in length. For either class of wait staff shifts may begin at any time of the day Mae chooses. 20:00 14 For example, a full-time staffer waiting tables could work from midnight to 8 AM, from 2:00 AM to 10:00 AM, 4:00 21:00 10 AM to noon, etc. Full-time wait staff are paid $9.55 per hour, with every hour worked from 10:00 PM till 6:00 AM 22:00 7 paying an additional $2.50 premium. Part-timers are paid a base rate of $8.35 per hour. \"I take care of my good people. 23:00 8 I pay better'n anybody around here for this kind of work,\" says Mae proudly. She remembers how hard it can be to support a family by waiting tables. Mae recognizes part time staff save Country Rose on wages, but she prefers full-timers. \"Them part-time people's just a pain in the neck!\" she says with exasperation. \"They don't know the job as well, and they don't show up to work, and they'll quit without tellin' you! Can you believe it? I've even had 'em come in knee-walkin' drunk and still expectin' to work! You can just count on full-timers better.\" a. Formulate and solve the mathematical programming model which will show Mae how to schedule the restaurant in the truck stop such that she her minimum staffing levels in each 1-hour block of while minimizing daily wage expense. Mae would part-time staff on duty at any time. meets time like no b. You'd like to convince Mae to use part-time staffers. She agrees to consider part-timers in her scheduling, but with two stipulations. These are 1) no more than eight part time wait staff may be in her restaurant at any given time, and 2) part-time staff can only be on the premises between 5 AM and 7 PM. These are Mae's usual working hours, so having part-timers work in this 14-hour stretch allows Mae to watch them. Following Mae's stipulations how much could be saved in daily wage expense if part-time staffers were used? 7. (25 pts.) Pacific Furniture of Santa Rosa, CA builds and markets a very small line of very high quality wooden outdoor furniture to both consumers and resorts. The furniture is primarily made of teak and comes in various styles and stains. The products of interest in planning manufacturing for the next year are: 1. 2. 3. The Cape Cod Beach Set Individual Cape Cod Chair The Quiet Chat Set 4. 5. The Occasional Table The Garden Fun Bar Set Cape Cod Beach Set Cape Cod Chair Quiet Chat Set Occasional Table Garden Fun Bar Set (Natural) Garden Fun Bar Set (Dark Stain) Major resources used in building the Pacific Furniture products are: 1. 2. 3. 4. 5. Cut Teak Wood ($6 per board foot) Skilled Woodworker Labor ($34 per hour) Unskilled Assembly Labor ($10 per hour) Equipment Time ($26 per hour) Dark Stain ($18 per gallon) Cape Cod Beach Set The Cape Cod Beach Set consists of two Cape Cod style chairs and a small table, all made from teak and treated with the dark stain. Building an entire set requires 90 board feet of teak, 8 hours of skilled woodworker labor, 1 hour of unskilled assembly labor, 2 hours of equipment time, and 1 1/2 quarts of dark stain. The set is sold for $4500. Cape Cod Chair This is the same design of chair as is used in the Cape Cod Beach Set but sold individually. Making one chair requires 31 board feet of teak, 3 hours of skilled woodworker labor, 1/3 hour of unskilled assembly labor, 3/4 hours of equipment time, and 1/4 quart of dark stain. The individual chair is sold for $1850. Quiet Chat Set The Quiet Chat Set consists of a single chair, a 3-person stationary bench, and a food table. Building the set requires 80 board feet of teak, 6 hours of skilled woodworker labor, 1 hour of unskilled assembly labor, 1 1/2 hours of equipment time, and 1 quart of dark stain. The set is sold for $3800. Occasional Table The Occasional Table is the same design as the food table sold in the Quiet Chat Set. Building the table requires 15 board feet of teak, 2 hours of skilled woodworker labor, 1/2 hour of unskilled assembly labor, and 1/2 hours of equipment time. The product is sold \"natural\" and as such requires no stain. The table is sold for $1325. Garden Fun Bar Set The Garden Fun Bar Set consists of a teak bar and two bar stools and is sold in both stained and natural versions. Building either version requires 50 board feet of teak, 4 hours of skilled woodworker labor, 1/2 hour of unskilled assembly labor, and 1 hour of equipment time. The dark stained version of the product requires 1 quart of stain. Whether natural or dark stained, the Garden Fun Bar Set sells for $3900. Next year Pacific Furniture will have available 400,000 board feet of teak, 30,000 hours of skilled woodworker labor time, 5,000 hours of unskilled assembly labor time, and 8,000 hours of equipment time. Stain is unlimited since it can be readily purchased from many sources. Additionally, management has imposed the following special restrictions: 1. The number of Garden Fun Bar Sets produced in natural and dark stain finishes should be equal. At least 18% of total product output should be Occasional Tables (calculated on a product-unit basis). At least 1000 units each should be produced of the Cape Cod Beach Sets and the Quiet Chat Sets. No more than 2500 Occasional Tables should be produced. At least 1100 Cape Cod Chairs should be produced. 2. 3. 4. 5. a b Use a mathematical programming model which will determine the proper product mix for Pacific Furniture which will maximize total contribution margin. Make sure your production quantities for each product are integer. Pacific Furniture has two separate opportunities: 1) acquire an additional lot of 50,000 board feet of teak, and 2) acquire an additional block of 2,000 unskilled labor hours. Should they take either or both of these opportunities