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A Brokerage House Offers Three Stock Portfolios

question 169

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A brokerage house offers three stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio III consists of 2 blocks of common stock, 1 municipal bond, and 3 blocks of preferred stock. A customer wants 16 blocks of common stock, 8 municipal bonds, and 6 blocks of preferred stock. Let x equal the number of units of Portfolio I, y equal the number of units of Portfolio II, and z equal the number of units of Portolio III. If the numbers of the three portfolios offered must be integers, find the general solution that can be used to determine all possible offerings. ​


Definitions:

Cost of Goods Sold

The overall expenses involved in creating or purchasing goods sold in a given timeframe, consisting of the cost of materials, workforce, and indirect costs.

Standard Cost

A set cost for producing either one unit or multiple units of a product within a defined timeframe, based on existing or expected operational circumstances.

Direct Materials

The raw materials that can be directly traced to the production of a specific product.

Direct Labor

The wages and other costs for labor that is directly involved in the production of goods or services.

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