Solve the linear programming problem.
-An automotive glass plant must be able to fill orders for 230 truck windshields, 350 auto windshields, and 310 RV windshields. Because the first-shift crews are more experienced, they are each able to make 7 truck
Windshields, 12 auto windshields, and 9 RV windshields. The second-shift crews are able to produce 4 truck
Windshields, 12 auto windshields, and 7 RV windshields. The first-shift crews cost the company $360.00 per
Crew per shift, and the second-shift crews cost $310.00 per crew per shift. The company's facilities will handle at
Most 50 crews on each shift, and they must have at least 10 crews come in to keep the plant running. How many
First-shift and how many second-shift crews should be scheduled to minimize costs?
A) 51 first-shift crews and 17 second-shift crews
B) 28 first-shift crews and 10 second-shift crews
C) 37 first-shift crews and 36 second-shift crews
D) 43 first-shift crews and 24 second-shift crews

Question

Quizplus · Accepted Answer

To solve this linear programming problem, we need to minimize the cost function while satisfying the constraints for the production of truck, auto, and RV windshields. The constraints include the production capabilities of both shifts and the minimum and maximum number of crews. By setting up the equations for the production requirements and applying the cost for each crew, option B (28 first-shift crews and 10 second-shift crews) is identified as the solution that meets the production needs while minimizing costs, given the information provided.

Solve the Linear Programming Problem