# Transportation, Assignment ,Integer Programming Problem

See attached file for full problem description.

13. Diet Mix Problem 1

The dietician for the local hospital is trying to control the calorie intake of the heart surgery patients. Tonight's dinner menu could consist of the following food items: chicken, lasagna, pudding, salad, mashed potatoes and jello. The calories per serving for each of these items are as follows: chicken (600), lasagna (700), pudding (300), salad (200), mashed potatoes with gravy (400) and jello (200). If the maximum calorie intake has to be limited to 1200 calories. What is the dinner menu that would result in the highest calorie in take without going over the total calorie limit of 1200.

a) chicken, mashed potatoes and gravy, jello and salad

b) lasagna, mashed potatoes and gravy, and jello

c) chicken, mashed potatoes and gravy, and pudding

d) chicken, mashed potatoes and gravy, and salad

14. Product Mix Problem 1

Danson furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?

Hint: There are two decision variables and two explicit constraints

a) $30,000 b) $43,500 c) $45,000 d) $54,000

19. Transportation Problem 1

A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

Find the optimal solution and determine how many cases should be shipped from factory C to Assembly Plant 3.

a) 35 b) 43 c) 54 d) 60

20. Transportation Problem 2

Consider the following transportation problem:

What is the total minimum transportation cost associated with this model?

a) $1550 b) $1600 c) $1700 d) $1725

21. Assignment Problem 1

The table above represents the average number of sales for each of three people (A, B, C) at each of four stores (1, 2, 3, 4). With three people and four stores, assigning one person per store will mean that one store is closed. Determine the number of combined sales that result when assignments of people to stores are maximized for sales.

a) 20 b) 22 c) 24 d) 26

25. Integer Programming Problem 1

Consider the following integer linear programming problem

The solution to the Linear programming relaxation is: x1 = 5.714, x2= 2.571.

What is the Z value for the optimal solution under integer constraints?

a) 18 b) 19 c) 20 d) 24

26. Mixed Integer Problem

The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

The objective cost function associated with this model is:

Min Z = 750y1 + 500y2 + 1000y3 + 300y4 + 1.25x1 + 1.5x2 + 1.0x3 + 2.0x4

( F i x e d C o s t s) + (V a r i a b l e C o s t s)

where yi = 1, if machine i is used, and xi = number of hoses produced on machine i.

Based on the optimal solution, what is the total minimum cost associated with this model?

HINT: There are five explicit constraints. The first four involve the capacity of each machine, and each of these first four constraints contains one x and one y variable. Each of these can be expressed as xi - ci*yi <= 0, where ci is the capacity of machine i. The fifth constraint is the contract constraint.

a) 13000 b) 13250 c) 13500 d) 13750

27. Integer Programming Problem 2

Find the Z value of the optimal solution

a) 50 b) 52 c) 54 d) 56

30. Transshipment Problem

The following diagram shows a transshipment network. Nodes 1, 2, and 3 are supply nodes. The supply values are to the left of these nodes. Nodes 6, 7, and 8 are demand (sink) nodes, and the demand values are to the right of these nodes. Transshipment routes between nodes are labeled with the transportation cost per unit.

What is the minimum transportation cost associated with this network?

a) 3220 b) 3470 c) 3610 d) 3780

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The word file provides mathematical formulation. Excel file contains optimal solution.