A retail store in Des Moines, Iowa, receives shipments of a particular product f

Question

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 the constraints.
e. State the mathematical model for satisfying the demand at the Des Moines retail store at
minimum cost.

Explanation / Answer

a.) total=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=x+y where x<=4000 and y<=3000 (<= means less than or equal to)

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 referall to part b, then use the equation demand=$.20x

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