# Determistic Optimization

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Deterministic Optimization
Homework 1
Problem 1 (40 Points). A wine Company produces two kinds of wine Nectar and Red.
The wines are produced from 64 tons of grapes the company has acquired this season. A
1,000-gallon batch of Nectar requires 4 tons of grapes, and a batch of Red requires 8 tons.
However, production is limited by the availability of only 50 cubic yards of storage space for aging and 120 hours of processing time. A batch of each type of wine requires 5 cubic yards of storage space. The processing time for a batch of Nectar is 15 hours, and the processing time for a batch of Red is 8 hours. Demand for each type of wine is limited to seven batches.
The proﬁt for a batch of Nectar is \$9,000, and the proﬁt for a batch of Red is \$12,000.
The company wants to determine the number of 1,000-gallon batches of Nectar and Red to produce in order to maximize proﬁt. a Formulate a linear programming model for this problem. b Solve this model by using graphical analysis. c How much processing time will be left unused at the optimal solution? d What would be the eﬀect on the optimal solution of increasing the available storage space from 50 to 60 cubic yards?
Problem 2 (60 Points). A manufacturing ﬁrm into two products. Each product may undergo three processes (assembly, ﬁnishing and packing). The ﬁrm has 2400 hours available for assembly and 800 hours for ﬁnishing,and 1200 hours for packing. Each unit of product
1 has a proﬁt of \$5 and requires 3 hours to assemble and 0 hours to ﬁnish and 2 hours to package. Each unit of product 2 has a proﬁt of \$2 and requires 2 hours to assemble and 1 hours to ﬁnish and 0 hours to package. The ﬁrm wants to determine the quantity of each product to produce in order to maximize proﬁt. a Formulate a linear programming model for this problem. b Use the graphical method to solve this…...

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