Reference no: EM133771378

Homework: Business- Operations Management

Question I: The manager Emily at Cozy Stitches has a team of 20 artisans: 6 Skilled knitters, 4 Junior knitters and 10 assistants, each of whom had a unique talent when it came to knitting sweaters.Wage structure for each artisan type is as follows: Skilled Knitters: $30 per hour, Junior Knitters: $25 per hour, Assistants: $20 per hour.

On average, each artisan worked for 8 hours a day, with breaks to rest their nimble fingers. On average, they produced 30 sweaters collectively each day. Beyond the wages and materials, the workshop incurred miscellaneous expenses to keep the operation running efficiently. These included the cost of quality wool and yarn, knitting needles, utilities, and maintenance of the knitting machines. On average, these miscellaneous expenses amounted to $500 per day.

With the additional demand, Emily started to think about purchasing a state-of-the-art knitting machine that would help the company meet the rising demand without compromising on quality. The machine is capable of knitting sweaters at an impressive speed and with great precision. The cost of operating themachine, including maintenance and electricity, on top of the previous miscellaneous expenses amounted to $100 per day.

With the machine, Cozy Stitches can produce an additional 50 sweaters per day, increasing their daily production from 30 to 80 sweaters. However, this change also meant that some of the artisans would have to be let go. Emily must make the difficult decision to terminate the employment of a few of the workers. After assessing the situation, she needs to let go of3 Skilled knitters, 2 junior knitters and 5 assistants.
Emily wants to determine the impact of the new machine on productivity. Answer the questions below based on the information provided. The productivity is measured as production output (no. of sweaters per day) per daily labor and additional expenses (in $ per day).

1. What is the current daily productivity level at Cozy Stitches?
2. What will be the daily productivity level at Cozy Stitches if Emily adapts the new machine?
3. What is the expected percentage change in daily productivity at Cozy Stitches if Emily adapts the new machine?

Question II: A manufacturing company produces expensive toys. Each toy sells for $200 and costs $75. The company incurs a fixed cost of $6,000 per day to lease their machines to manufacture the toys. Depending on the volume of production the company mustalso hire and scheduleenough number of employees to carry out the production. The additional labor costs are $500, $1000 and $2500 per day, when the production volume is 0 to 30 units, 31 to 60 units, and 61 to 90 units per day, respectively. The company forecasts the daily expected demand for its toys to be 75 units.

1. Compute the break-even point for each range of production volume separately.

2. Which production volume range is the best for the company? Explain clearly why.

3. Suppose the company has a production capacity of 85 units per day. (Use this information independent of the production volumes mentioned above). What is (i) the capacity cushion and (ii) the capacity utilization; if the company decides to produce only as much as the demand forecast?

Question III: A brewerysells three types of beer: Lager, Pale Ale and Stout. Each barrel of Lager requires 0.6 units of malt, 0.2 units of hops and 0.1 units of yeast; each barrel of Pale Ale requires 0.7 units of malt, 0.3 units of hops and 0.2 units of yeastand; each barrel of Stout requires 0.8 units of malt, 0.4 units of hops and 0.3 units of yeast. The brewery has 200 units of malt, 80 units of hops and 50 units of yeast available each month.According to an already signed contract with the local retailer, the brewery should sendat least 150 barrels of Lager, at least 100 barrels of Pale Ale and at least 75 barrels of Stout each month. Because of the capacity constraints at the retailer,the brewery cannot send more than 200 barrels of Lager, more than 125 barrels of Pale Ale and more than 100 barrels of Stout each month. The brewery makes a profit of $10 per barrel of Lager, $8 per barrel of Pale Ale and $12 per barrel of Stout.

You are asked to determine the optimal product mix that maximizes the monthly total profit. You will formulate a linear programming model. You will NOT solve this problem by Excel Solver.

Show all your work one piece of paper.

1. What are the decision variables? How many decision variables are there? Clearly explain the decision variables in English and provide the mathematical notation used in the algebraic formulation of the decision problem.

2. What is the objective function? Clearly explain the objective function in English and provide the mathematical formulation.

3. What are the constraints of the problem? Clearly explain each constraint in English and provide the mathematical formulation.

4. Are there any sign or type restrictions in your formulation? Why or why not? Clearly explain the sign and type restrictions (if any).