Thread: Business Math

1. Business Math

1. 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
1. 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?

The three verticies show where a max can occur.

Checking near each one( they are not all integers)

we get

15 glass trays 0 decanters
12 glass trays 3 decanters
1 glass tray 6 decanters

plugging each of these into the profit function gives

$\displaystyle P(g,d)=50d+10g$
$\displaystyle P(15,0)=50(0)+10(15)=150$
$\displaystyle P(12,3)=50(3)+10(12)=270$
$\displaystyle P(1,6)=50(6)+10(1)=310$

So the most profit occus with 6 decanters and 1 glass tray.

for b and the constraint that $\displaystyle g \ge 5$

find your new vertices and repeat the same process.

I hope this helps.

Good luck