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a cake shop sells cakes and cupcakes. a cake uses 5 cups of cake batter. a batch of cupcakes uses 4 cups of batter. the pastry chef has 40 cups of cake batter and wants to make at least 4 cakes. the profit on a cake is $35 and the profit for a batch of cupcakes is $30. How many cakes and batches of cupcakes should the pastry chef make in order to maximize profits? what is the maximum revenue?

Sagot :

Chef should prepare 4 cakes and 5 batches of pastry in order to achieve maximum profits and his maximum profit or revenue by solving through inequality is $260.

Given Chef uses 5 cups of cake batter for 1 cake and 4 cups of batter for 1 batch of cupcakes. Chef wants to make at least 4 cakes. Profit on 1 cake is $35 and $30 for 1 batch of cupcake.

let the number of cakes be x and the number of batches of cupcakes be y such that

5x+4y<=40--------1

x>=4---------------2

Maximize Profit=35x+30y

Inequalities contains different signs so we have to change one inequality.

5x+4y<=40

-x<=-4

Now assume them equalities

5x+4y=40-------3

-x=-4

multiply second equations by 5

-5x=-20-----------4

now  add 3 and 4

5x+4y-5x=40-20

4y=20

y=5

now put the value of y in 5x+4y=40

5x+4*5=40

5x+20=40

5x=20

x=4.

Maximum Profit=35x+30y

=35*4+30*5

=$260

Hence chef should make 4 cakes and 5 batches of pastry and maximum profit of $260.

Learn more about inequality at https://brainly.com/question/11613554

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