Question 5.p.4: A manager must decide which type of equipment to buy, Type A...
A manager must decide which type of equipment to buy, Type A or Type B. Type A equipment
costs $15,000 each, and Type B costs $11,000 each. The equipment can be operated 8 hours a day, 250 days a year.
Either machine can be used to perform two types of chemical analysis, C1 and C2. Annual service requirements and processing times are shown in the following table. Which type of equipment should be purchased, and how many of that type will be needed? The goal is to minimize total purchase cost.
| PROCESSING TIME PER ANALYSIS (hr) |
|||
| Analysis Type | Annual Volume | A | B |
| C1 | 1,200 | 1 | 2 |
| C2 | 900 | 3 | 2 |
Total processing time (Annual volume × Processing time per analysis) needed by type of equipment:
| Analysis Type | A | B |
| C1 | 1,200 | 2400 |
| C2 | Total \frac{2,700}{3,900} | \frac{1,800}{4,200} |
Total processing time available per piece of equipment is 8 hours/day × 250 days/year = 2,000.
Hence, one piece can handle 2,000 hours of analysis, two pieces of equipment can handle 4,000 hours, and so on.
Given the total processing requirements, two of Type A would be needed, for a total cost of 2 × $15,000 = $30,000, or three of Type B, for a total cost of 3 × $11,000 = $33,000. Thus, two pieces of Type A would have sufficient capacity to handle the load at a lower cost than three of Type B.