RBMC Industry manufactures a special printing according to customer specifications with respect to the number of sheets the machine can produce per hour. With this, there is a $50 increase in the production rate x. A shop owner is considering buying one of these machines. From his past experiences, the owner estimates that the arrival rate is three per hour and each order averages 500 sheets. Contracts signed by the owner, and the customer says that there will be a penalty of 10$ per late order per hour. It is assumed that the actual production time is exponential. (a) Formulate the cost model as a function of the production rate x. (b) Determine the optimal production rate the owner should specify in his purchase of the machine from RBMC. Hint: Get the derivative of the cost function.
[Queuing Theory - Operations Research]
RBMC Industry manufactures a special printing according to customer specifications with respect to the number of sheets the machine can produce per hour. With this, there is a $50 increase in the production rate x. A shop owner is considering buying one of these machines. From his past experiences, the owner estimates that the arrival rate is three per hour and each order averages 500 sheets. Contracts signed by the owner, and the customer says that there will be a penalty of 10$ per late order per hour. It is assumed that the actual production time is exponential.
(a) Formulate the cost model as a function of the production rate x.
(b) Determine the optimal production rate the owner should specify in his purchase of the machine from RBMC. Hint: Get the derivative of the cost function.
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