Question

A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $4000 when sold. A ranch style house requires $40,000 of capital and provides an $8000 profit. If the contractor has $3.6 million of capital on hand, how many houses of each type should she build for maximum profit? Will any of the lots be vacant?

Answer 1

If the contractor builds only colonial homes, she can build 120 homes with the $3.6 million of capital on hand. If the contractor builds only ranch style homes, she can build 90 homes with the $3.6 million of capital on hand. To maximize profit, the contractor should build 90 ranch style homes and 30 colonial homes, for a total of 120 homes. This will produce a profit of $1,080,000 ($90,000 from the 30 colonial homes and $990,000 from the 90 ranch style homes). This leaves 10 lots vacant.