A manufacturer produces two models of elliptical cross-training exercise machines. The times for assembling,finishing,and packaging model X are 3 hours,3 hours,and 0.8 hour,respectively.The times for model Y are 4 hours,2.5 hours,and 0.4 hour.The total times available for assembling,finishing,and packaging are 6000 hours,4200 hours,and 950 hours,respectively.The profits per unit are $200 for model X and $275 for model Y.What is the optimal production level for each model? What is the optimal profit?

A)6000 units of model X 950 units of model Y
Optimal profit: $1,461,250
B)950 units of model X 6000 units of model Y
Optimal profit: $1,840,000
C)400 units of model X 1200 units of model Y
Optimal profit: $410,000
D)950 units of model X 4200 units of model Y
Optimal profit: $1,345,000
E)4200 units of model X 950 units of model Y
Optimal profit: $1,101,250

Question

A manufacturer produces two models of elliptical cross-training exercise machines. The times for assembling,finishing,and packaging model X are 3 hours,3 hours,and 0.8 hour,respectively.The times for model Y are 4 hours,2.5 hours,and 0.4 hour.The total times available for assembling,finishing,and packaging are 6000 hours,4200 hours,and 950 hours,respectively.The profits per unit are $200 for model X and $275 for model Y.What is the optimal production level for each model? What is the optimal profit?
​
A)6000 units of model X 950 units of model Y
Optimal profit: $1,461,250
B)950 units of model X 6000 units of model Y
Optimal profit: $1,840,000
C)400 units of model X 1200 units of model Y
Optimal profit: $410,000
D)950 units of model X 4200 units of model Y
Optimal profit: $1,345,000
E)4200 units of model X 950 units of model Y
Optimal profit: $1,101,250

Quizplus · Accepted Answer

The optimal production level is 400 units of model X and 1200 units of model Y, which satisfies the constraints for assembling, finishing, and packaging times while maximizing the profit.

A Manufacturer Produces Two Models of Elliptical Cross-Training Exercise Machines