Thread: a- Write the simplex matrix to maximize the profit.

1. a- Write the simplex matrix to maximize the profit.

Hello:
I need to Write the simplex matrix to maximize the profit in the following problem:

A contractor builds two types of homes. The Carolina model requires one lot, $160,000 in capital, and 160 worker-days of labor and the Savannah model requires one lot,$240,000 in capital, and 160 worker-days of labor. The contractor owns 300 lots, has $48,000,000 available capital, and has 43,200 available worker- days of labor. The profit on the Carolina model is$40,000. The profit on the Savannah model is $50,000. Find how many of each type of home should be built to maximize profit. my answer is: Maximize: F = 40,000x + 50,000y, subject to : x + y ≤ 300 160,000x + 240,000y ≤ 48,000,000 160x + 160y ≤ 43,200 is that correct? my textbook tells me that's not correct, I don't understand why. thank you. 2. Originally Posted by jhonwashington Hello: I need to Write the simplex matrix to maximize the profit in the following problem: A contractor builds two types of homes. The Carolina model requires one lot,$160,000 in capital, and 160 worker-days of labor and the Savannah model requires one lot, $240,000 in capital, and 160 worker-days of labor. The contractor owns 300 lots, has$48,000,000 available capital, and has 43,200 available worker- days of labor. The profit on the Carolina model is $40,000. The profit on the Savannah model is$50,000. Find how many of each type of home should be built to maximize profit.

Maximize: F = 40,000x + 50,000y, subject to :
x + y ≤ 300
160,000x + 240,000y ≤ 48,000,000
160x + 160y ≤ 43,200

is that correct? my textbook tells me that's not correct, I don't understand why.

thank you.

Recheck the question, if what you have type is correct, then the constraint $\displaystyle x+y\le 300$ is not relevant as $\displaystyle 160x + 160y \le 43,200$ is always stricter. Also you have not given the non-negativity constraints $\displaystyle x \ge 0$ and $\displaystyle y\ge 0$

CB