Pierre-Hadrien is a pastry chef in the Parisian restaurant L'Excuse that serves crois- sants and palmiers for breakfast. Pierre-Hadrien needs to work under the daily prod- ucts' constraints imposed by the restaurant's owner. He sets up a linear optimization problem to maximize the restaurant's revenue from the sales of croissants and palmiers. Palmiers are sold for $4 each and croissants for $5 each. (Yes, ok, these should be € but let's pretend a French cafe would accept $ for the sake of this exercise.) We assume that Pierre-Hadrien can sell all the palmiers and croissants he produces. Croissants and palmiers' production require various quantities of butter, sugar, our and eggs as specifed in the table below. Palmiers Croissant Total Supplies per day Butter (g) 200 100 15000 Sugar (g) 200 300 25000 Flour (g) 100 200 17000 Eggs (units) 0.4* 0.6* 35 *Note that eggs are in decimals because pastry chefs typically bake the paste for multiple pastries at once. A paste with 3 eggs can then produce 5 croissants. Your objective is to help Pierre-Hadrien maximizing his revenue using a linear optimization model. (a) Specify the decision variables, the objective function and the constraints for the model. You may assume that fractional values for the number of palmiers and croissants are acceptable. (b) Is the decision to make 30 palmiers and 50 croissants per day feasible? Why or why not? (c) Pierre-Hadrien wants to be loyal to the customers who prefer croissants. Specify one constraint that can be added to the model that will ensure that at least 14 croissants are produced each day. (d) Is the claim \the objective value must increase as a result of adding the constraint in (c)" correct?
Pierre-Hadrien is a pastry chef in the Parisian restaurant L'Excuse that serves crois-
sants and palmiers for breakfast. Pierre-Hadrien needs to work under the daily prod-
ucts' constraints imposed by the restaurant's owner. He sets up a linear optimization
problem to maximize the restaurant's revenue from the sales of croissants and palmiers.
Palmiers are sold for $4 each and croissants for $5 each. (Yes, ok, these should be €
but let's pretend a French cafe would accept $ for the sake of this exercise.) We assume
that Pierre-Hadrien can sell all the palmiers and croissants he produces. Croissants
and palmiers' production require various quantities of butter, sugar, our and eggs as
specifed in the table below.
| Palmiers | Croissant | Total Supplies per day | |
| Butter (g) | 200 | 100 | 15000 |
| Sugar (g) | 200 | 300 | 25000 |
| Flour (g) | 100 | 200 | 17000 |
| Eggs (units) | 0.4* | 0.6* | 35 |
*Note that eggs are in decimals because pastry chefs typically bake the paste for
multiple pastries at once. A paste with 3 eggs can then produce 5 croissants.
Your objective is to help Pierre-Hadrien maximizing his revenue using a linear
optimization model.
(a) Specify the decision variables, the objective function and the constraints
for the model. You may assume that fractional values for the number of palmiers
and croissants are acceptable.
(b) Is the decision to make 30 palmiers and 50 croissants per day feasible?
Why or why not?
(c) Pierre-Hadrien wants to be loyal to the customers who prefer croissants.
Specify one constraint that can be added to the model that will ensure that at
least 14 croissants are produced each day.
(d) Is the claim \the objective value must increase as a result of adding the
constraint in (c)" correct?
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