A company makes two types of biscuits: Jumbo and Regular....

A company makes two types of biscuits: Jumbo and Regular. The oven can cook at most 300 biscuits per day. Each jumbo biscuit requires 2 oz of flour, each regular biscuit requires 1 oz of flour, and there is 500 oz of flour available. The income from each jumbo biscuit is $0.13 and from each regular biscuit is $0.09. How many of each size biscuit should be made to maximize income? What is the maximum income? The company should make jumbo and regular biscuits. The maximum income is $ .

Transcript

00:01 Hi, now we are going to find what is the maximum income.

00:05 Let x be the number of jumbo biscuits and y be the number of regular biscuits.

00:32 Now the given information is totally the company made 400 biscuits per day at most.

00:40 So we have x plus y is less than or equal to 400.

00:45 And another given information is each jumbo biscuit required 2 o's of flour and each regular biscuit requires 1 o's of flour and there is 500 o's of flour.

00:58 So we have 2x plus y is less than or equal to 500.

01:06 And the income function z will be 0 .13x plus 0 .08y.

01:15 Now we have to maximize this z.

01:21 Now the given two inequalities can be written as x plus y is equal to 400 and i label this one as equation number 1 and the second inequality can be written as 2x plus y is equal to 500 and i label this one as equation number 2.

01:40 Now in the equation 1, if i put x is equal to 0, then the value of y will be 400.

01:48 If i put y is equal to 0, then the value of x will be 400.

01:55 So the points of equation 1 are 0, 400 and 400, 0.

02:06 And next in the equation 2, if i put x is equal to 0, then the value of y will be 500.

02:17 If i put y is equal to 0, then the value of x will be 250.

02:24 So the points of equation 2 are 0, 500 and 250, 0.

02:37 And next we have to find the feasible region.

02:41 For that i am going to draw the above two lines in the graph.

02:47 Then we get this graph...

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