Caroline has several options for how to spend her Saturday night, listed in order of descending preference: 1. Go to a folk music concert with a friend. 2. Get dinner with several of her sorority sisters. 3. Go shopping with her mom. Caroline can only do one activity. Match each activity (on the left) with its opportunity cost (on the right).

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?