Question:

Must show all calculations$/$steps

correct. FOUR PLACES AFTER THE DECIMAL POINT $($except when all succeeding digits are

zeros.$)$

Atkinson Food Restaurant $($AFR$)$ makes four different diet nutrition meals for people who are willing to

lose weight, which are Meal A$,$ Meal B$,$ Meal C$,$ and Meal D$.$ The profit contribution, ingredients usage

$($Spice$,$ Eggs, Vegetables, and Chicken$),$ and cost are shown in the following table.

The manager of AFR has checked refrigerators and reveals that the restaurant has on hand $2,000$ grams of

stock of Spice, $18,000$ grams of eggs, $36,000$ grams of vegetables, and $64,000$ grams of chicken.

Four goals that AFR is now targeting: the primary goal of AFR is to approximately maximize the profit to

$$2,500,$ ideally more than that. Like any other entrepreneur, the secondary goal is to minimize the cost to

$$10,000,$ ideally less than that. The remaining two goals are relevant to eggs and chicken. The third goal

is the manager wants to control the use of eggs approximately to the current on$-$hand stock level of $18,000$

grams, ideally less than that. Lastly, the manager is willing to control the use of chicken approximately to

the current on$-$hand stock level of $64,000$ grams, not ideally more than or less than that. The manager is

now trying to formulate a goal$-$programming model.

a$)$ Clearly specify the deviation variables.

b$)$ Write all constraints using deviation variables defined in part $($a$).$ The store manager has defined

decision variables: A $=$ number of orders of Meal A$,$ B $=$ number of orders of Meal B$,$ C $=$ number

of orders of Meal C$,$ and D $=$ number of orders of Meal D$.$

c$)$ Write the objective function for this goal programming model assuming the above goals are in the

same priority level.

d$)$ Suppose that a shortage of eggs when AFR runs a regular business negatively impacts brand

reputation and customer satisfaction. Therefore, the manager would like to minimize the number

of eggs that are in shortage. Which deviation variable$/$s that is$/$are defined in part a$)$ will be

affected in this scenario?

$)$ Suppose the manager wants to achieve these goals in three different priorities. The manager

believes that priority level $1$ is to ideally have a profit of more than $$2,500($Goal $1).$ The priority

level $2$ is to ideally have the cost less than $$10,000($Goal $2).$ The priority level $3$ includes the

remaining two goals of eggs and chicken; however, the manager thinks that Goal $3$ is twice as

important as Goal $4.$ Specify all change$/$s on priority level $3$ problem compared to when the

manager wrote priority level $2$ problem.