A team of students has entered a robot competition, in which their robot must start from a base location, move to and grab objects, and return them to the base to score points. The point values assigned to the objects are 100, 50, and 25 points, depending on their distance from the base. There is a 4-minute time limit for the competition; only objects returned to the base will be counted in the scoring. The team has practiced retrieving all 10 objects; times for completing the round trip to the object and bringing it back to the base, along with the point values of each, are shown in Table P10.9.

Use Excel Solver to determine the objects that should be retrieved within the 4-minute time limit in order to maximize the team’s score.

Hint: The independent variables in this problem will be the number of each object that is retrieved. Since there is only one of each, the value of each independent variable will be either one or zero. Therefore, the constraints will be that each value is less than or equal to one, each value is an integer, and each value is non-negative. These constraints can be added in groups. For example, you can add a new constraint in Solver, select the range of cells containing all of the independent variables, and enter the constraint that all are less than or equal to one in one step.