Final answer:
To find the highest possible score Bridget and Andrew could earn in their ice skating routine, we can use the time and move constraints to solve an optimization problem. The highest score is 105 points, which can be achieved by performing 6 spins and 6 lifts.
Step-by-step explanation:
To determine the highest possible score Bridget and Andrew could earn, we need to find the combination of spins and lifts that maximizes their score within the given time and move constraints. Let's define two variables, x for spins and y for lifts, to represent the number of each move.
Since the routine can last for a maximum of 2 minutes, or 120 seconds, and each spin takes 10 seconds and each lift takes 15 seconds, we can write the equation 10x + 15y ≤ 120 to represent the time constraint.
Next, since they are allowed to complete a total of 10 or fewer moves, we can write the equation x + y ≤ 10 to represent the move constraint.
To find the highest possible score, we need to optimize the objective function which is the total score. The score for each spin is 5 points and for each lift is 7 points. So the objective function is 5x + 7y.
To solve this optimization problem, we can graph the feasible region formed by the intersection of the two constraints and find the corner point with the highest value of the objective function.
After solving the equations, we find that the highest possible score is 105 points and it can be achieved by performing 6 spins and 6 lifts.