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A Computer Start-Up Named Pear Is Considering Entering the U

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A computer start-up named Pear is considering entering the U.S. market with what they believe to be a smaller and faster computer than some of the existing products on the market. They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product. They want to collect a reasonable sample from across the U.S. representative of all age brackets. They have split the U.S. into 2 regions: East and West. They want to at least 65% of their sample to cover the East and no fewer than 25% of the West. They also have divided the age groups into 3 categories: 18-35, 36-69, and 70 and up. They want at least 50% of their sample to be between 18-35 and at least 40% to be between 36-69. The costs per person surveyed is given in the table below: A computer start-up named Pear is considering entering the U.S. market with what they believe to be a smaller and faster computer than some of the existing products on the market. They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product. They want to collect a reasonable sample from across the U.S. representative of all age brackets. They have split the U.S. into 2 regions: East and West. They want to at least 65% of their sample to cover the East and no fewer than 25% of the West. They also have divided the age groups into 3 categories: 18-35, 36-69, and 70 and up. They want at least 50% of their sample to be between 18-35 and at least 40% to be between 36-69. The costs per person surveyed is given in the table below:   Assume that exactly 1,000 people are to be surveyed. The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements. Formulate this problem as a linear program. Assume that exactly 1,000 people are to be surveyed. The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements. Formulate this problem as a linear program.

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Definitions:

Par Value

A nominal or face value assigned to a share of stock by the company's charter, which has little bearing on its market value.

Shares

Units of ownership in a company, representing a portion of the corporation's capital, often traded on stock exchanges.

Treasury Shares

Shares that were once part of the float and outstanding shares but were subsequently bought back by the issuing company, reducing the amount of stock on the open market.

Common Stock

Equity ownership in a corporation, with privileges that may include voting rights and a share in profits through dividends and capital appreciation.

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