Help!!!! System of Linear Inequalities

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gottalive4today

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A bakery sells pies and cakes. Each pie takes 20 minutes to prepare and 45 minutes to cook. Each cake takes 30 minutes to cook and a total of 40 minutes to mix and decorate. In a given day, the bakery has 16 hours of employee time for food preparation and 3 ovens available for 8 hours of each. The bakery makes a profit of $5.50 on each pie and $6.00 on each cake.


a) Let x = the number of pies and y = the number of cakes the bakery makes in a given day. Translate a system of linear inequalities.
c) Find the number of each dessert the bakery should make each day to max its profit.
 
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gottalive4today said:
A bakery sells pies and cakes. Each pie takes 20 minutes to prepare and 45 minutes to cook. Each cake takes 30 minutes to cook and a total of 40 minutes to mix and decorate. In a given day, the bakery has 16 hours of employee time for food preparation and 3 ovens available for 8 hours of each. The bakery makes a profit of $5.50 on each pie and $6.00 on each cake.


a) Let x = the number of pies and y = the number of cakes the bakery makes in a given day. Translate a system of linear inequalities.
c) Find the number of each dessert the bakery should make each day to max its profit.
Click to expand...

You have a given maximum of oven time and (pre & post) prep (employee) time. You have a profit equation. Show us what you have done.
 
gottalive4today said:
I am lost. I have no clue how to start.
Click to expand...

Let's start with the 'hint': Let x = the number of pies and y = the number of cakes the bakery makes in a given day. Translate a system of linear inequalities.

For a single pie we have
(a) 20 minutes prep
(b) 45 min to cook
(c) $5.50 profit
So for x pies we have
(a) 20 x minutes prep
(b) 45 x min to cook
(c) $5.50 x profit

For a single cake we have
(a) 40 minutes prep
(b) 30 min to cook
(c) $6.00 profit
So for y cakes we have
(a) 40 y minutes prep
(b) 30 y min to cook
(c) $6.00 y profit


Total prep (employee) time available = 16 hrs = 960 min
Total oven (bake) time available = 3 * 8 = 24 hrs = 1440 min

Total prep time needed = 20 x + 40 y
Total oven time needed = 45 x + 30 y
Total profit available = 5.50 x + 6 y

Can you go from there?
 
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