A certain company is interested in maximizing the monthly profit from two of its products, designated I and II. To manufacture these products the company uses a type of machine that has an availability of 200 machine-hours per month and a hand type of workforce with an availability of 240 man-hours per month. To produce a unit of product I, 5 machine hours and 10 labor hours are required, while for the product II, 4 hours of labor are used. Demand for 20 units is expected per month of product I and 45 units of product II. A profit per unit of US$ 10.00 is calculated for product I and US$ 6.00 for product II. Determine the quantities of each product which must be manufactured per month, for the maximum monthly profit.

Question

A certain company is interested in maximizing the monthly profit from two of its products, designated I and II. To manufacture these products the company uses a type of machine that has an availability of 200 machine-hours per month and a hand type of workforce with an availability of 240 man-hours per month. To produce a unit of product I, 5 machine hours and 10 labor hours are required, while for the product II, 4 hours of labor are used. Demand for 20 units is expected per month of product I and 45 units of product II. A profit per unit of US$ 10.00 is calculated for product I and US$ 6.00 for product II. Determine the quantities of each product which must be manufactured per month, for the maximum monthly profit.

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