Ms. waller receives orders for posy bouquets and cascade bouquets. it usually takes her 15 minutes to make one posy bouquet and 20 minutes to make one cascade bouquet. for today's orders, each posy bouquet must have 12 stems and each cascade bouquet must have 6 stems. ms. waller has no more than 300 minutes to make the bouquets, and she can procure no more than 180 stems in all. ms. waller makes a profit of $10 on each posy bouquet and $7 on each cascade bouquet. how many posy bouquets and cascade bouquets should she deliver to maximize her profit?

Ms. Waller should deliver 12 posy bouquet and 6 cascade bouquets.

Explanation:

Let the number of delivered posy bouquet be x and The number of delivered cascade bouquets be y. So,

It is given that it usually takes her 15 minutes to make one posy bouquet and 20 minutes to make one cascade bouquet. Ms. Waller has no more than 300 minutes to make the bouquets.

For today's orders, each posy bouquet must have 12 stems and each cascade bouquet must have 6 stems and she can procure no more than 180 stems in all.

Ms. Waller makes a profit of $10 on each posy bouquet and $7 on each cascade bouquet.

So we have to maximise the value of Z.

Subject to the constants,

    ..... (1)

       ..... (2)

   .... (3)

Plot these inequalities on a coordinate plane as shown below.

Solve equation (1) and (2) by elimination method to find the intersection point of both lines.

On solving (1) and (2), we get x=12 and y=6.

The vertex of shaded region are (0,0),(15,0),(12,6) and (0,15).

Check the value of Z on each vertex.

The value of Z are 0,150,162 and 105 on (0,0),(15,0),(12,6) and (0,15) respectively.

Therefore, the maximum profit is 162 on (12,6). It means Ms. Waller should deliver 12 posy bouquet and 6 cascade bouquets to maximise her profit.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?