As you will see in a later chapter, forces are vector quantities, and the total force on an object is the vector sum of all forces acting on it. In the figure below, a force
F1
of magnitude 5.90 units acts on an object at the origin in a direction θ = 33.0° above the positive x-axis. A second force
F2
of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction (in degrees counterclockwise from the +x-axis) of the resultant force
F1 + F2.

Two forces act on an object. Force vector F1 acts up and right on the right side of the object at an acute angle θ above the horizontal. Force vector F2 acts vertically upwards on the top side of the object.
magnitude
units
direction
° counterclockwise from the +x-axis

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)