Set up the linear programming problem.An office manager is buying used filing cabinets. Small file cabinets cost $4 each and large file cabinets cost $11 each, and the manager cannot spend more than $98 on file cabinets. A small cabinet takes up 6 square feet of floor space and a large cabinet takes up 10 square feet, and the office has no more than 108 square feet of floor space available for file cabinets. The manager must buy at least 6 file cabinets in order to get free delivery. Let x = the number of small file cabinets bought and y = the number of large file cabinets bought. Write a system of inequalities that describes these constraints.
A. 4x + 11y ? 98
6x + 10y ? 108
x + y ? 6
B. 4x + 11y ? 98
6x + 10y ? 108
y ? 6
C. 4x + 11y ? 98
10x + 6y ? 108
x ? 6
D. 4x + 11y ? 98
6x + 10y ? 108
x + y ? 6
Answer: D
Mathematics
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