Question

In: Operations Management

Jo Anna will bake some brownies for the next Work day. She will make two different...

Jo Anna will bake some brownies for the next Work day.

She will make two different kinds: oatmeal and chocolate chip. Everyone knows

that the chocolate is a crowd favorite, so she wants the number of chocolate chip

cookies to be twice as much the number of oatmeal cookies. Additionally, she

needs at least eight dozen cookies. She estimates she will spend $0.25 per

oatmeal cookie and $0.35 per chocolate chip cookie. Additionally, she has

limited amount of butter, sugar, and flour in her kitchen and she does not have

time to go back to the grocery store. She estimates the amount of material

required for each cookie and measures her available material:

Amount Required in grams Availability in grams

oatmeal chocolate

Butter 9.46 6.31 700

Sugar 8.33 5.55 1000

Flour 5.00 10.00 850

(she is comfortable with the Standard!)

a. (Linear Programming) How many cookies of each type she should bake to

minimize her cost?

b. (Integer Programming) If she has to batch her cookies as a dozen, how

many dozen of each type she should bake?

Please show in exel show formulas and use solver

Expert Solution

(a)

Excel model:

Solver inputs:

Solution:

	Oatmeal cookies	Chocolate cookies
Dozens of	2.49	5.51
Cost	$3.00	$4.20	$30.61
s.t.
Ratio	-2	1	0.521	>=	0
Min total	1	1	8.000	>=	8
Butter	113.52	75.72	700.000	<=	700
Sugar	99.96	66.60	615.971	<=	1000
Flour	60.00	120.00	810.413	<=	850

So,

The no. of oatmeal cookies = 2.49 doz = 29.88 units
The no. of chocolate cookies = 5.51 doz = 66.12 units

(b)

Keep everything else the same and only add the integer constraint in Solver as follows:

Solution:

	Oatmeal cookies	Chocolate cookies
Dozens of	2	6
Cost	$3.00	$4.20	$31.20
s.t.
Ratio	-2	1	2.000	>=	0
Min total	1	1	8.000	>=	8
Butter	113.52	75.72	681.360	<=	700
Sugar	99.96	66.60	599.520	<=	1000
Flour	60.00	120.00	840.000	<=	850

So,

The dozens of oatmeal cookies = 2
The dozens of chocolate cookies = 6

keosha answered 6 months ago

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