Question

1. The manufacturing department of the Thomas Lee Company is planning

its production level over the next six months. Based on orders received and
sales forecasts provided by the marketing department, the estimate of
monthly demand forecast for the twelve-month period is as follows:
Month
1
2 3
Forecasted Demand (000) 16 19 10
4 5
16
18
6
17
The monthly unit holding cost is $4, the cost of hiring a worker is $3000; the
cost of laying off a worker is $2000. Regular employee works 40 hours per
week with monthly salary of $3200 and the cost of utilizing overtime is 1.5
times the regular time labor cost. Each worker can produce 50 units per
month during regular time and each worker can work no more than 10 hours
of overtime per week. Current starting inventory is 500 units, the initial
workforce level is 150 and the maximum physical production capacity is
20000 units per month. We may assume that there are 4 weeks in a month.
Thomas Lee would like to find the optimal (i.e., least cost) production plan.
(a) (15 points) Formulate a linear program to solve this problem. Define
your decision variables and explain the constraints.
(b)(15 points) Solve the linear program.

Answer 1

The best production method when labor costs $100/unit and capital costs $400/unit is Method 1 with a total cost of $9,000. If the cost of labor rises to $200/unit, Method 1 is still the most cost-effective option, now at $13,000.

Step-by-step explanation:

The subject of this question is determining the best production method based on costs for labor and capital. When the cost of labor is $100/unit and the cost of capital is $400/unit, the costs for each method are as follows:

• Method 1: (50 x 100) + (10 x 400) = $9,000
• Method 2: (20 x 100) + (40 x 400) = $18,000
• Method 3: (10 x 100) + (70 x 400) = $29,000

Therefore, Method 1 is the cheapest option at this price level. If the cost of labor increases to $200/unit, the new costs will be:

• Method 1: (50 x 200) + (10 x 400) = $13,000
• Method 2: (20 x 200) + (40 x 400) = $18,000
• Method 3: (10 x 200) + (70 x 400) = $29,000

Even with the increased labor costs, Method 1 remains the most cost-effective option.