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A drug company produces regular flu and "swine" flu vaccines. Flu vaccines are designed every year by experts in anticipation of the flu season and are manufactured only during the month of September. During that month the company has capacity to manufacture up to 300,000 total vaccine doses (regular plus swine). Demand for regular flu vaccines far exceeds their capacity. They want to decide how many doses of swine flu vaccine to produce. Any remaining capacity will be used to produce regular flu doses. The contribution of each regular flu vaccine is $9. Swine Flu vaccines have a per-dose cost of $6 and sell for $30. By law, any leftover swine flu vaccines at the end of the season must be destroyed by the company, which represents an additional unit cost of $10. Assume demand for the swine flu vaccine doses is random with the following discrete distribution:

Flu vaccine doses Probability 10,000 .10 20,000 .05 30,000 .05 40,000 .03 50,000 .02 60,000 .02 70,000 .03 80,000 .02 90,000 .03 100,000 .02 110,000 .03 120,000 .10 130,000 .15 140,000 .10 150,000 .15 160,000 .05 170,000 .03 180,000 .02

Answer :

The drug company produces regular flu and swine flu vaccines during the month of September. manufacturing capacity of 300,000 doses, the company wants swine flu vaccine to produce the demand and profitability.

Regular flu vaccines have high demand, and any remaining capacity will be used for regular flu doses. Swine flu vaccines have a lower cost but also a risk of excess inventory due to legal requirements for destruction. The demand for swine flu vaccines follows a discrete distribution.

To optimize the production and maximize profitability, the drug company needs to carefully consider the demand for both regular flu and swine flu vaccines. The primary objective is to meet the high demand Cost of underage for regular flu vaccines while minimizing the risk of excess inventory for swine flu vaccines.

Using the discrete distribution of swine flu vaccine demand, the company can calculate the expected demand and revenue for different production quantities of swine flu vaccines. By considering the cost per dose, selling price, and the additional unit cost of destroying leftover doses, they can assess the profitability at various production levels.

The company needs to strike a balance between producing enough swine flu vaccines to capture the market opportunity and avoiding excessive production that would lead to losses due to destruction costs. By analyzing the demand probabilities and associated revenue, they can determine the optimal quantity of swine flu vaccines to produce within the available capacity.

Ultimately, the decision should aim to maximize the overall profitability of the company by efficiently utilizing the manufacturing capacity and meeting the demand for both regular flu and swine flu vaccines.

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