Solve the linear programming problem.
-An automotive glass plant must be able to fill orders for 230 truck windshields, 350 auto windshields, and $310 \mathrm { RV }$ windshields. Because the first-shift crews are more experienced, they are each able to make 7 truck windshields, 12 auto windshields, and $9 \mathrm { RV }$ 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) 43 first-shift crews and 24 second-shift crews
C) 28 first-shift crews and 10 second-shift crews
D) 37 first-shift crews and 36 second-shift crews

Question

Quizplus · Accepted Answer

To solve this linear programming problem, we need to minimize the cost function subject to the constraints given by the production requirements and the limitations on the number of crews. The correct answer is found by setting up the equations for the production of each type of windshield, the cost function, and the constraints on the number of crews, then solving these equations to find the combination of first-shift and second-shift crews that minimizes cost while meeting all production and constraint requirements. The choice that fits these criteria is 28 first-shift crews and 10 second-shift crews, as it is the most cost-effective solution that satisfies all the given conditions.

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