Quantitative Analysis for Management, 13/e

Solved Problems

1. Solved Problem 9-1 Don Yale, president of Hardrock Concrete Company, has plants in three locations and is currently working on three major construction projects, located at different sites. The shipping cost per truckload of concrete, plant capacities, and project requirements are provided in the accompanying table.

   Formulate Hardrock’s transportation problem as a linear program and solve using software.

   TO FROM	PROJECT A	PROJECT B	PROJECT C	PLANT CAPACITIES
   PLANT 1	$10	$4	$11	70
   PLANT 2	$12	$5	$8	50
   PLANT 3	9	$7	$6	30
   PROJECT REQUIREMENTS	40	50	60	150

   Solution

   Define the variables as

   $$X_{ij}=\text{number of units shipped from Plant }i\text{ to Project }j$$

   where

   $$\begin{array}{l}i\text{ = 1, 2, 3 with 1 = Plant 1, 2 = Plant 2, and 3 = Plant 3}\\ j\text{ = 1, 2, 3 with 1 = Project A, 2 = Project B, and 3 = Project C ...}\end{array}$$