Question 67901: My math problem is broken up into check points in my book.
Check point 1) A company manufactures bookselves and desks for computers. Let x represent the numbers of bookselves manufactured daily and y the number of desks manufactured daily. The company's profits are $25 per a bookshelf and $55 per desk. Write the objective function that describes the company's total profit, z, from x bookselves and y desks.
Check point 2) To maintain high quality, the company in check point 1 should not manufacture more than a combined total of 80 bookselves and desks per day. Write an inequality that describes this constraint.
Check point 3) To meet consumer demand, the company in check point 1 must manufacture between 30 and 80 bookselves per day, inclusive. Furthermore, the company must manufacture between 10 and no more than 30 desks per day. Write an inequality that describes each of these sentences. Then summarize what you have described about this company by write the objective function for it's profits, and the three constraints.
Check point 4) For the company in check points 1-3, how many bookselves and how many desks should be manufactured per day to obtain a maximum profit? What is the maximum daily profit?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Check point 1) A company manufactures bookselves and desks for computers. Let x represent the numbers of bookselves manufactured daily and y the number of desks manufactured daily. The company's profits are $25 per a bookshelf and $55 per desk. Write the objective function that describes the company's total profit, z, from x bookselves and y desks.
z=25x+55y
----------------------
Check point 2) To maintain high quality, the company in check point 1 should not manufacture more than a combined total of 80 bookselves and desks per day. Write an inequality that describes this constraint.
x+y<=80
------------------------------
Check point 3) To meet consumer demand, the company in check point 1 must manufacture between 30 and 80 bookselves per day, inclusive. Furthermore, the company must manufacture between 10 and no more than 30 desks per day. Write an inequality that describes each of these sentences. Then summarize what you have described about this company by write the objective function for it's profits, and the three constraints.
30<=x<=80
10<=y<=30
Check point 4) For the company in check points 1-3, how many bookselves and how many desks should be manufactured per day to obtain a maximum profit? What is the maximum daily profit?
x+y<=80
Graph y<=-x+80
--------------------
30<=x<=80
Draw vertical lines at x=30 and x=80
--------------------
10<=y<=30
Draw horizontal lines at y=10 and y=30
------------------------
Find the intersection of the equality lines:
If x=30, y=50 (30,50)
---
If y=10, x=70 (70,10)
-----------
z=25x+55y
Check these point values in the object equation:
Point (30,50) : z=25*30 + 55*50 = $3500
Point (70,10) : z=25*70 + 55*10 = $2300
__________
Profit is maximized if 30 bookshelves and 50 desks are produced.
Cheers,
Stan H.
|
|
|
