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A retail store in Des Moines, Iowa, receives shipments of a particular product from Kansas City and Minneapolis. Let x = number of units of the product received from Kansas City y = number of units of the product received from Minneapolis a. Write an expression for the total number of units of the product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost $0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines. c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model for satisfying the demand at the Des Moines retail store at minimum cost. Solve using linear programming

Sagot :

The expression for the total number of units of the product received is x + y.

How to depict the information?

The total will be =y+x because it will be the sum of the two shipment quantities.

b. Cost = $.20(x)+$.25(y) because the cost will be the sum of the costs per unit for each shipment.

c. 5000 =x+y allows for any combination of x and y units.

d. Total will be: x+y where x<=4000 and y<=3000

e. The minimum cost is where a and b are minimized in demand =ax+by. We cannot determine a maximum value for a or b because we do not know what the demand is. If the problem calls for referral to part b, then use the equation demand=$.20x

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