Question

The Production Supervisor for a Manufacturing firm is planning the production of two electronic devices: Radio's (R) and Sensors (S). Two resources are constrained: production time (1), of which he has at most 400 minutes per day, and electronics (E), of which he can get at most 900 minutes per day. To build a Radio requires 2 minutes of production time and 5 minutes of electronics time, and to build a Sensor it requires 3 minutes of production time and 6 minutes of electronics time. Profits for the Radios are $4.00 per unit and profits for the Sensors are $3.00 per unit Given all of this information: • The objective function is: Max Z = $4 R + $3 S •

Answer 1

The concept of economies of scale is demonstrated by the cost per unit decreasing as production volume increases. A small factory producing fewer units has higher costs per unit than a larger factory producing more units. This concept applies to the manufacture of electronics, where maximizing profits is balanced against resource constraints.

Step-by-step explanation:

Economies of Scale in Production

The concept of economies of scale relates to the cost advantages that a business obtains due to scale of operation, with cost per unit of output generally decreasing with increasing scale as fixed costs are spread out over more units of output. In the context provided, a small-sized factory like 'S' producing 1,000 alarm clocks has an average cost of $12 per clock. If a factory scales up to a 'medium' size like 'M' and produces 2,000 alarm clocks, the average cost per clock falls to $8. Further scale to a 'large' size like 'L' with an output of 5,000 clocks would reduce the average cost per clock even more, to $4. This illustrates how larger production volumes can lead to lower average costs due to economies of scale.

Applying this understanding to the production of electronic devices such as Radios (R) and Sensors (S) by a manufacturing firm, there are constraints on production - specifically, the production time and electronics materials available. This scenario requires careful planning to maximize profits (referred to as the objective function, Max Z = $4R + $3S), while adhering to resource constraints (400 minutes of production time and 900 minutes of electronics time available per day). As the output level increases, the firm may also experience economies of scale, potentially decreasing the average cost per unit and improving profitability.