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A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit?

a. B = 400; C = 1000; Max Z = $380
b. B = 500; C = 900; Max Z = $350
c. B = 250; C = 1500; Max Z = 425
d. B = 300; C = 750; Min Z = $380

Respuesta :

Answer:

x₁  =  400    x₂  =   1000

z(max)  =  380 $

Step-by-step explanation:

Production:

                                      Flour      yeast     Almond paste      Profit $

Bear claws B  (x₁)            6 ou       1 ou            2 TS                   0.2

Almond-filled ( x₂)          3 ou       1  ou           4 TS                   0.3

Availability                    6600      1400           4800

The Model:

z  =   0.2*x₁   +  0.3*x₂       to maximize

Subject to

1.-Quantity of flour   6600 ou

6*x₁  +  3*x₂   ≤  6600

2.-Quantity of yeast  1400 ou

1*x₁   +   1*x₂   ≤  1400

3.-Quantity of Almond paste   4800 TS

2*x₁   +  4*x₂   ≤  4800

General constraints:

x₁ ≤  0    x₂  ≤ 0   both integers

After 6 iterations using an on-line solver. Optimal solution is:

x₁  =  400    x₂  =   1000

z(max)  =  380 $

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