Given: An “unbalanced” transportation problem, where the supply of aggregate is not equal to the demand.

You are in charge of a large construction project that involves two sites. You currently need 50 tons of aggregate at site 1 and 22 tons of aggregate at site 2. Two suppliers are available, and their limits are listed below. Restrictions on the type of work to be done require that at least 20 tons used at site 1 have to come from supplier B and no more than 10 tons of aggregate from supplier A can be used at site 2. Aggregate delivery costs ($/ton) are as follows:

Delivery Costs: |
To Site1 |
To Site 2 |

From Supplier A |
$1/ton |
$2/ton |

From Supplier B |
$1.5/ton |
$1.25/ton |

Required:

a) Solve this problem as an “unbalanced” transportation problem where the supply exceeds demand, assuming that Supplier A can deliver up to 31 tons, and Supplier B can deliver up to 43 tons.

b) Solve as an “unbalanced” transportation problem where the available supply is less than the demand, assuming that Supplier A can deliver a maximum of 27 tons, and Supplier B can deliver a maximum of 43 tons.