Posted by **Tushar** on Monday, February 25, 2008 at 4:49pm.

The Wellbuilt Company produces two types of wood chippers, Deluxe and Economy.

The Deluxe model requires 3 hours to assemble and ½ hour to paint, and the Economy

model requires 2 hours to assemble and 1 hour to paint. The maximum number of

assembly hours available is 24 per day and the maximum number of painting hours

available is 8 per day. If the profit on the Deluxe model is $15 per unit and the profit on

the Economy model is $12 per unit, how many units of each model will maximize profit?

Let x = number of Deluxe models

y = number of Economy models

a. List the constraints

b. Determine the objective function. __________________

c. Graph the set of constraints. Place number of Deluxe models on the horizontal axis

and number of Economy models on the vertical axis.

d. Find the vertices of the feasible region.

Vertices Profit

e. How many Deluxe models and how many Economy models should the Wellbuilt

Company produce to maximize their profit?

Deluxe____________

Economy__________

f. What is the maximum profit? __________________

- Math - Linear Inequalities -
**Reiny**, Monday, February 25, 2008 at 5:15pm
Using your definitions:

3x+2y ≤ 24 (assembly restraint) and

.5x+y ≤ 8 (painting restraint), alos

x ≥ 0 and y ≥ 0

Profit = 15x+12y

Solving the two corresponding equations above gave me (4,6)

so the vertices of your feasible region would be (0,0) (don't make any at all, silly)

(0,8) and (16,0)

"Sliding" the profit equation P=15x+12y, which has a slope of -5/4 away from the origin, while maintaining the slope would reach the point (4,6) of your region.

Can you tie all this together, and reach the correct answers?

- Math - Linear Inequalities -
**Tushar**, Monday, February 25, 2008 at 5:38pm
Ok I understand the constratints, Can you please explain me how you got feasible region (0,0), (0,8) and (16,0).

And also slope -5/4.

Thanks for your help

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