Question: Consider the following linear program where X1, X2, and X3represent the number of gourmet cookies, brownies, and cakes sold by Littons Bakery on a weekly

Consider the following linear program where X1, X2, and X3represent the number of gourmet cookies, brownies, and cakes sold by Littons Bakery on a weekly basis. They profit $25 from cookies, $15 from brownies, and $35 per cake. The bakery has the following constraints.

They are limited to 500 pounds of flour

They must use at least 450 grams of sugar (or else it will go bad)

They cannot use more than 400 oz of oil

They need to produce at least 40 batches of cookies for charity

Using the output below, answer the questions on the next page

MAX 25X1+15X2+35X3

S.T. 1) 4X1+2X2+4X3<500

2) 3X1+3X2+5X3>450

3) 2X1+1X2+3X3<400

4) 1X1>40

OPTIMAL SOLUTION

Objective Function Value = 3975.000

Variable Value Reduced Costs

-------------- --------------- ------------------

X1 40.000 0.000

X2 0.000 2.500

X3 85.000 0.000

Constraint Slack/Surplus Dual Prices

-------------- --------------- ------------------

1 0.000 8.750

2 95.000 0.000

3 65.000 0.000

4 0.000 -10.000

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

------------ --------------- --------------- ---------------

X1 No Lower Limit 25.000 35.000

X2 No Lower Limit 15.000 17.500

X3 30.000 35.000 No Upper Limit

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit

------------ --------------- --------------- ---------------

1 424.000 500.000 586.667

2 No Lower Limit 450.000 545.000

3 335.000 400.000 No Upper Limit

4 0.000 40.000 87.500

How many cookies, brownies, and cakes should Littons bakeeach week?

How much profit will Littons make?

How many grams of sugar will be used?

If 20 extra pounds of flour were available, what impact what that have on Littons profit?

If Littons charged $30 per cake instead of $35, how many cakes should they plan to bake?

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