macho_bob
Joined: 02 Dec 2007
Posts: 7
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 Posted: Sun Dec 02, 2007 7:05 am Post subject: Maximization problem? |
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| I'm having a problem with math. We are doing maximization problems and I think this problem gives us too much info, I keep trying to use all of it though. Can someone start me off??A retired couple earns extra money by making two kinds of wedding cakes in their home. The husband mixes the pastry dough and the wife does the finishing and baking of the cakes.The husband can mix at most 18 cakes per week and the wife can bake no more than 20. A typical type 1 cake takes 2 hours of mixing and 4 hours baking.Type 2 cake takes 3 hours of mixing and 2 hours of finishing and baking. The profit for cake 1 is $40 and the profit for type 2 is $30. How many cakes should the couple make to maximize profit. Solve by graphing.I don't understand why they say how many hours the cakes take, why does that matter??Thank you for any help you can give me. |
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lils
Joined: 02 Dec 2007
Posts: 5
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| Posted: Sun Dec 02, 2007 9:29 am Post subject: Maximization problem? |
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Let a = # of type 1 cake made per week, b = # of type 2 cake made per weekMax Profit = 40a + 30b subject to constraintsa + b <= 18 (largest number of cakes that husband can mix per week is 1 a + b <= 20 (largest number of cakes that wife can bake per week is 20)2a + 3b <= 168 (number of hours husband can work per week)4a + 2b <=168 (number of hours wife can mix per week)where there are 168 hours in a week (7 days, 24 hrs) |
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