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Linear Production : Production Planning

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Production Planning. The Bogard Corporation produces three types of bookcases, which it sells to large office supply companies. The production of each bookcase requires two machine operations, trimming and shaping, followed by assembly, which includes inspection and packaging. All three type require 0.4 hour of assembly time, but the machining operations have different processing times, as shown here, in hours per unit.

Standard Narrow Wide
Timmer 0.2 0.4 0.6
Shaper 0.6 0.2 0.5

Each Machine is available 150 hours per month, and the current size of the assembly department provides capacity of 600 hours. Each bookcase produced yields a unit profit contribution as follows:

Standard Narrow Wide
Profit $8 $6 $10

a. What are the optimal production quantities for the company?

b. What is the pattern in the optimal allocations?

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Solution Summary

Solution shows the optimal production quantities for the company and the pattern of the optimal allocations.

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Computer Production Planning via Linear Programming

A laptop manufacturer is developing a production schedule for the next four quarters. Demands for this manufacturer's laptop computer are forecasted to be 1200 in quarter 1; 2100 in quarter 2; 1500 in quarter in 3; and 600 in quarter 4. Assume that it costs this manufacturer $1200 to produce each laptop computer. At the end of each quarter, a holding cost of $300 per computer left in inventory is incurred. Increasing production from quarter to the next incurs costs for hiring and training new employees. It is estimated that a cost of $2100 per computer is incurred if production is increased from one quarter to the next. Decreasing production from one quarter to the next incurs costs for lying off employees, loss of morale, and so forth. It is estimated that a cost of $1800 per computer is incurred if production is decreased from one quarter to the next. All demands must be met on time, and the units produced in one quarter can be used to meet demand for the current quarter as well as for future quarters. During the quarter immediately preceding quarter 1 (e.g., the most recent quarter), 1000 laptop computers were produced. Assume that at the beginning of quarter 1 no computers are in inventory.

Help the computer manufacturer formulate and solve a linear programming spreadsheet model to find the production schedule that minimizes total cost over the given planning horizon.

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