Question

University Games produces two types of computer games - adventure and fantasy. One adventure game requires 200 hours of time from the creative staff and 500 hours from the tech staff. One fantasy game requires 400 hours of time from the creative staff and 100 hours from the tech staff. The company has 16,800 hours of creative staff and 6,000 hours of tech staff. Formulate a system of equations to determine how many games of each type should be produced to use all staff time.

a) 30 adventure games and 12 fantasy games.
b) 40 adventure games and 10 fantasy games.
c) 20 adventure games and 15 fantasy games.
d) 25 adventure games and 14 fantasy games.

Answer 1

The system of equations is created based on the hours required for each type of game by the creative and tech staff, which are then set equal to the total available staff hours to find the needed production quantities.

Step-by-step explanation:

To formulate a system of equations for the number of adventure games (A) and fantasy games (F) University Games should produce to utilize all staff time, we use the information given about the time required for each type of game:

• An adventure game requires 200 hours of creative staff and 500 hours of tech staff.
• A fantasy game requires 400 hours of creative staff and 100 hours of tech staff.

The total available hours for the creative staff are 16,800 hours and for the tech staff are 6,000 hours. Therefore, we can set up the following system of equations:

200A + 400F = 16,800 (Equation for creative staff time)

500A + 100F = 6,000 (Equation for tech staff time)

To find the solution that uses all the staff time without leaving any idle time, we solve these equations simultaneously.