1. Quantitative Method for Business--MATH HELP!!!

I need help solving and setting up this problem. I have gotten the first 3 problems, but this #4 is really difficult for me. I need help to solve and set this problem up. Please any help would be appreciated.

4. A glass blower makes glass decanters and glass trays on a weekly basis. Work in progress cannot be carried over from week to week. Each item requires 1 pound of glass, and the glass blower has 15 pounds of glass available each week. A glass decanter requires 4 hours of labor, a glass tray requires 1 hour of labor, and the glass blower works 25 hours a week. The profit from a decanter is $50, and the profit from a tray is$10.

a. Find the optimal production schedule for this situation.

b. If the glass blower received an order for 5 trays that she could not refuse, what would be the optimal production schedule?

c. What would be the penalty for this additional constraint?

2. Originally Posted by darkdesign007
I need help solving and setting up this problem. I have gotten the first 3 problems, but this #4 is really difficult for me. I need help to solve and set this problem up. Please any help would be appreciated.

4. A glass blower makes glass decanters and glass trays on a weekly basis. Work in progress cannot be carried over from week to week. Each item requires 1 pound of glass, and the glass blower has 15 pounds of glass available each week. A glass decanter requires 4 hours of labor, a glass tray requires 1 hour of labor, and the glass blower works 25 hours a week. The profit from a decanter is $50, and the profit from a tray is$10.

a. Find the optimal production schedule for this situation.

b. If the glass blower received an order for 5 trays that she could not refuse, what would be the optimal production schedule?

c. What would be the penalty for this additional constraint?
Formulate the problem:

Let the number of decanters be d, and trays be t.

d>=0, t>=0.

Glass mass constraint: d+t<=15

Labour constaint: 4d+t<=25

Objective; maximise the profit p=50d+10t

RonL