Question

Rework problem 27 in section 1 of Chapter 7 of your textbook, about the greenhouse operator, using the following data. Assume that each Type 1 layout uses 36 tulips, 24 daffodils, and 8 flowering shrubs; that each Type 2 layout uses 12 tulips, 42 daffodils, and 7 flowering shrubs; and that each Type 3 layout uses 22 tulips, 52 daffodils, and 5 flowering shrubs. Assume also that the greenhouse operator has on hand 1110 tulips, 890 daffodils, and 94 flowering shrubs. Assume also that the profit on each Type 1 layout is $85.00, the profit on each Type 2 layout is $40.00, and the profit on each Type 3 layout is $90.00.
How many layouts of each type of should the greenhouse operator plant in order maximize its profit?

Answer 1

Answer:

one of the first

then sixteen of the third.

none of the second

Explanation:

We can solve by hand using legrande multiplier

and derivate or we can use the solver tool of excel:

1) we build up a table on excel with the data for each layout

Then, we use solver.

We declare the quantity of each unit as out variable

the total profit as our goal to maximize

we stablish the restrictions based on our inventory at hand

And excel determinates that 16 of the third layout and one of the first layout will yield the greater profit

SOLVER  

Q tulips daffodils flowerings PROFIT per layout

1          36       24 8                    84

0           12       42 7                    40

16           22       52 5                    90

Totals 388     856 88      

used   (16 x 22 + 36) (16 x 52 + 24)   (  16 x 5 + 8)

Total profit: 1524

(16 x 90 + 84)