Linear Programming- Manufacturing - NEED HELP

[Nate_zz.inc]

Here is the problem...

One of the dolls at Dolls R Us is Talking Tommy. Another doll without the talking mechanism is called Silent Sally. In one hour, the company can produce 8 Talking Tommy dolls or 20 Silent Sally dolls. Because of the demand, the company knows that it must produce at least twice as many Talking Tommy dolls as Silent Sammy dolls. The company spends no more than 48 hours per week making these two dolls. The profit on each Talking Tommy doll is $3.00, and the profit on each Silent Sally is $7.50.

a. How many of each doll should be produced to maximize profit each week?

b. What is the profit?

This is really tough, and I would really appreciate help.

 

[stapel]

One of the dolls at Dolls R Us is Talking Tommy. Another doll without the talking mechanism is called Silent Sally. In one hour, the company can produce 8 Talking Tommy dolls or 20 Silent Sally dolls. Because of the demand, the company knows that it must produce at least twice as many Talking Tommy dolls as Silent Sammy dolls. The company spends no more than 48 hours per week making these two dolls. The profit on each Talking Tommy doll is $3.00, and the profit on each Silent Sally is $7.50.

a. How many of each doll should be produced to maximize profit each week?

b. What is the profit?

This is really tough, and I would really appreciate help.

We'll be glad to help, but we'll need to know where you're getting stuck. Your class has studied linear optimization (like here). You've noted that they're asking you for the numbers of dolls, so you've picked variables for these items. You've noted the normal constraints (namely, that you can't produce negative numbers of dolls). You've set up inequalities in terms of the relative numbers of dolls and the number of hours per work-week. You've graphed the feasibility region, plugged corner points into the optimization equation, and... then what?

Please be complete. Thank you!