### Dairy company produces a broad line of dairy products

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The Delight Dairy Company produces a broad line of dairy products. For production planning purposes, the company has been aggregated into two major products: Ice Cream and Specialties such as ice cream sandwiches and pre packaged ice cream. Both products have its own packagingarrow-10x10.png machine but use a common, single ice cream manufacturing machine and the same pool of labor.

The ice cream requires two hours of the ice cream machinearrow-10x10.png, one hour on its own packagingarrow-10x10.png line, and three labor-hours to produce 1,000 gallons of finished product.

The Specialty products requires one hour of the ice cream machine, one hour on its own packaging line, and six labor hours to produce the equivalent of 1,000 gallons of finished product. One thousand gallons of ice cream can be sold for \$900, and the equivalent of 1,000 gallons of specialties can be sold for \$1,500.

The company currently works a one-shift operation (40 hours per week) and currently employs three full-time employees and one ¾ - time employee.

a. Formulate a linear programming arrow-10x10.png model for production planning for Delight Dairy Company.

b. Solve the problem graphically. Show the feasible region, all corner points, and include the derivation of both from the LP-problem you set up in part a.

c. Now, suppose that 10 additional labor-hours could be made availablearrow-10x10.png by hiring that part time employee as a full time one. What does this do to the solution? Show the result graphically.

d. Refer to the original case described in (a). Suppose competition has forced the price of ice cream down from \$900 to \$600 for 1,000 gallons. Would this change the product plan for the company? If so, what would be the new plan?

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