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# Decision making under constriants.

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Gluth Company makes three products in a single facility. These products have the following unit product costs (PLEASE SEE THE ATTACHED FILE FOR THE DATA):

The mixing machines are potentially the constraint in the production facility. A total of 23,200 minutes are available per month on these machines.
Direct labor is a variable cost in this company.

Required:
a. How many minutes of mixing machine time would be required to satisfy demand for all four products?
b. How much of each product should be produced to maximize net operating income? (Round off to the nearest whole unit.)
c. Up to how much should the company be willing to pay for one additional hour of mixing machine time if the company has made the best use of the existing mixing machine capacity? (Round off to the nearest whole cent.)

#### Solution Summary

The solution shows how to make decisions under situations of constraint.

Constraint resources are resources that limit the amount of production in a company.

\$2.19

## Linear Programming : Finding Constraints

Please formulate the constraints for this problem as well as solutions to parts c and d.

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Round Tree Manor is a hotel that has two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit contribution per night for each type of room and rental class is as follows:

(see attached file for chart)

Type I rooms do not have Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit could be used to determine the number of reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms.

a. Formulate a linear programming model that can be used to determine the number of reservations to accept in each rental class and how these reservations should be allocated to room types.

b. Determine the number of reservations that can be accommodated in each rental class and whether the demand by any rental class is not satisfied.

c. Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost to Round Tree Manor of providing the breakfast is \$5, determine if this incentive should be offered.

d. With a little work, an unused office area could be converted to a rental room. Assuming that the conversion cost is the same for both types of rooms, provide a recommendation and explanation for converting the office to a Type I or a Type II room.
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