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Acompany manufactures x units of product a and y units of product b, on two machines, i and ii. it has been determined that the company will realize a profit of $3 on each unit of product a and $4 on each unit of product b. to manufacture a unit of product a requires 7 min on machine i and 5 min on machine ii. to manufacture a unit of product b requires 8 min on mchine i and 5 min on machine ii. there are 175 min available on machine i and 125 min available on machine ii in each work shift. how many units of a product should be produced in each shift to maximize the company's profit p?

By 2020, automobile market analysts expect that the demand for electric autos will increase as buyers become more familiar with the technology. however, the costs of producing electric autos may increase because of higher costs for inputs (e.g., rare earth elements), or they may decrease as the manufacturers learn better assembly methods (i.e., learning by doing). what is the expected impact of these changes on the equilibrium price and quantity for electric autos?

Suppose a country's productivity last year was 84. if this country's productivity growth rate of 5 percent is to be maintained, this means that this year's productivity will have to be: