6. A Housing Development 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 left vacant?
Added by Victoria P.
Close
Step 1
Let x be the number of colonial houses and y be the number of ranch-style houses. Show more…
Show all steps
Your feedback will help us improve your experience
Oluwadamilola Ameobi and 97 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A contractor is starting a new housing development consisting of colonial, split-level, and ranch-style houses. A colonial house requires ½ acre of land, $60,000 capital, 4000 labor hours to construct, and returns a profit of $20,000. A split-level house requires ½ acre of land, $60,000 capital, 3000 labor hours to construct, and returns a profit of $18,000. A ranch house requires 1 acre of land, $80,000 capital, 4000 labor hours to construct, and returns a profit of $24,000. The contractor has 30 acres of land, $3,200,000 capital, and 180,000 labor hours available. How many of each type of house should be constructed to maximize profit? What is the maximum profit?
Carson M.
A housing contractor designed two styles of houses: bungalows and 2-story houses for 100 available lots. The bungalows style requires P1.5M capital and produces a profit of P200,000 when sold. A 2-story house requires P2M capital and will earn a profit of P400,000. If the available capital on hand is P180M, how many houses of each type should be built to gain a maximum profit?
Madhur L.
A contractor builds two types of homes. The first type requires one lot, $12,000 capital, and 150 labor-days to build and is sold for a profit of $24,000. The second type of home requires one lot, $32,000 capital, and 200 labor-days to build and is sold for a profit of $34,000. The contractor owns 150 lots and has available 24,000 labor-days. How many of each type of home should she build to realize the greatest profit? Identify the objective function. Graph constraints, identify vertices, and find the optimal solution. Complete sensitivity analysis on coefficients of variables in the objective function. Complete sensitivity analysis on constants of constraint functions. Find the shadow price.
Julian W.
Recommended Textbooks
Precalculus with Limits
Precalculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD
Precalculus educators are ready to help you.