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?

a.

ms. waller should make 15 posy bouquets and 0 cascade bouquets to maximize her profit.

b.

ms. waller should make 6 posy bouquets and 12 cascade bouquets to maximize her profit.

c.

ms. waller should make 12 posy bouquets and 6 cascade bouquets to maximize her profit.

d.

ms. waller should make 0 posy bouquets and 15 cascade bouquets to maximize her profit.

A.  Ms. Waller should make 15 posy bouquets and 0 cascade bouquets to maximize her profit.

Step-by-step explanation:

Let x be the number of posy bouquet and y be the number of cascade bouquet.

Given,

The time taken for making a posy bouquet = 15 minutes,

And, the time taken for making a cascade bouquet = 20 minutes,

Thus, the total time taken = 15x + 20y,

Since, no more than 300 minutes is taken to make the bouquets,

⇒ 15x + 20y ≤ 300

Now, each posy bouquet must have 12 stems and each cascade bouquet must have 6 stems,

So, the total number of stems = 12x + 6y,

There must be no more than 180 stems in all,

⇒ 12x + 6y ≤ 180,

Now, we have to maximize the profit if each posy bouquet has $ 10 profit and each cascade bouquet has $ 7 profit.

⇒ Total profit = 10x + 7y,

Now, the numbers of bouquets can not be negative,

⇒ x ≥ 0 and y ≥ 0

Thus, there is a LPP that represents the given situation for which the function that must be maximize is,

Z = 10x + 7y,

And, the subject of constraints are,

15x + 20y ≤ 300; 12x + 6y ≤ 180,

x ≥ 0, y ≥ 0

By graphing the above inequalities,

We found that,

The vertex points of the feasible region are,

(0,0), (15,0) and (0,20),

Since, at (0,0), the profit would be,

Z = 10 × 0 + 7 × 0 = 0 + 0 = 0

At (15,0), the profit would be,

Z = 10 × 15 + 7 × 0 + 150 + 0 = 150

At (0,20), the profit would be,

Z = 10 × 0 + 7 × 20 = 0 + 140 = 140

Hence, the profit would be maximum when x = 15 and y = 0,

That is, Ms. Waller should make 15 posy bouquets and 0 cascade bouquets to maximize her profit.  

Option A is correct.

yes the data was not prsented

step-by-step explanation: