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Question Statement

A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is $5.50 and the price per unit of the Illinois corn is $6.00

The objective function that represents the total cost can be formulated = TC = 5.5x1 + 6x2

A constraint equation that the manufacturer needs at least 12000 units of corn can be formulated = x1 + x 2 >=12000

A constraint equation that the Iowa cooperative can supply up to 8000 units can be formulated = x1 <= 8000

A constraint that the Illinois cooperative must supply at least 6000 units can be formulated = x1 <= 6000

Discussion Question

Discuss how the objective function that represents the total cost can be formulated = TC = 5.5x1 + 6x2

Discuss how the constraint equation that the manufacturer needs at least 12000 units of corn can be formulated = x1 + x 2 >=12000

Solution

z = TC = 5.5x1 + 6x2

To maximise Z, subject to x1 + x 2 >=12000and

x1 <= 8000

x2 <= 6000

Consider the critical points (8000,4000) (6000,6000)

For I one z = 5.5(8000)+36000 = 80000

For II z = 69000

z is minimum for x1 =6000 and x2 =6000