The Enormous State University's Business School is buying computers. The school has two models to choose from. Each first model comes with 400 MB of memory and 80 GB of disk space, while each second model has 300 MB of memory and 100 GB of disk space. For reasons related to its accreditation, the school would like to be able to say that it has a total of at least 48,000 MB of memory and at least 12,800 GB of disk space. If both models cost $4,400 each, how many of each should the school buy to keep the cost as low as possible What are the shadow costs of memory and disk space
A)80 first models and 60 second models, $ $\frac { 77 } { 6 }$ per MB and $ $\frac { 385 } { 8 }$ per GB
B) 60 first models and 80 second models, $ $\frac { 385 } { 8 }$ per MB and $ $\frac { 385 } { 8 }$ per GB
C) 60 first models and 80 second models, $ $\frac { 77 } { 6 }$ per MB and $ $\frac { 385 } { 8 }$ per GB
D) 60 first models and 80 second models, $ $\frac { 77 } { 6 }$ per MB and $ $\frac { 77 } { 6 }$ per GB
E) 80 first models and 60 second models, $ $\frac { 385 } { 8 }$ per MB and $ $\frac { 77 } { 6 }$ per GB

Question

The Enormous State University's Business School is buying computers. The school has two models to choose from. Each first model comes with 400 MB of memory and 80 GB of disk space, while each second model has 300 MB of memory and 100 GB of disk space. For reasons related to its accreditation, the school would like to be able to say that it has a total of at least 48,000 MB of memory and at least 12,800 GB of disk space. If both models cost $4,400 each, how many of each should the school buy to keep the cost as low as possible  What are the shadow costs of memory and disk space  
A)80 first models and 60 second models, $ $\frac { 77 } { 6 }$ per MB and $ $\frac { 385 } { 8 }$ per GB
B) 60 first models and 80 second models, $ $\frac { 385 } { 8 }$ per MB and $ $\frac { 385 } { 8 }$ per GB
C) 60 first models and 80 second models, $ $\frac { 77 } { 6 }$ per MB and $ $\frac { 385 } { 8 }$ per GB
D) 60 first models and 80 second models, $ $\frac { 77 } { 6 }$ per MB and $ $\frac { 77 } { 6 }$ per GB
E) 80 first models and 60 second models, $ $\frac { 385 } { 8 }$ per MB and $ $\frac { 77 } { 6 }$ per GB

Quizplus · Accepted Answer

To minimize cost while meeting the requirements, we can set up a system of inequalities based on the memory and disk space requirements and solve for the number of each model needed. The correct combination that meets the requirements at the lowest cost is 60 first models and 80 second models. The shadow costs, which represent the additional cost per unit of a resource (memory or disk space) if the requirement is increased by one unit, are correctly calculated as $ $\frac { 77 } { 6 }$ per MB for memory and $ $\frac { 385 } { 8 }$ per GB for disk space in option C.

The Enormous State University's Business School Is Buying Computers 776\frac { 77 } { 6 }677​

The Enormous State University's Business School Is Buying Computers $\frac { 77 } { 6 }$