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[](https://)# HW1
**Group 20**
**Group Members:**
Clytze Sun, Gavin Hsu, Yun-yung Wang
## Q1.
Let $x_1$ = percentage of beef in a patty, $x_2$ = percentage of pork in a patty

a.
**Objective Function:**
min $0.85x_1+0.65x_2$

s.t.
$x_1, x_2 \geq 0$
$x_1 + x_2 = 1$
$0.2x_1 + 0.3x_2 \leq 0.25$

b.
![](https://i.imgur.com/YMzbBDB.png)
**Formulas:**

B8 = $B$5+$B$6
B9 = $B$5 * $C$2+$B$6 * $C$3

c. 
Minimum Cost way: 0.5 of beef and 0.5 of pork in a patty, which get $0.75 per patty

## Q2.
Let $x_1$ = amount of country table, $x_2$ = amount of contemporary table

a. 
**Objective Function:**
Max $350x_1 + 450x_2$

s.t. 
$x_1, x_2 \geq 0$
$x_1 \geq (x_1+x_2) \times 0.2$
$x_2 \geq (x_1+x_2) \times 0.3$
$(1.5x_1 + 2x_2) \leq 1000$
$(3x_1 + 4.5x_2) \leq 2000$
$(2.5x_1 + 1.5x_2) \leq 1500$

b.
![](https://i.imgur.com/Px1BIJc.png)
**Formulas:**
B8 = 1.5 * B5
B9 = 3 * B5
B10 = 2.5 * B5

C8 = 2 * C5
C9 = 4.5 * C5
C10 = 1.5 * C5

D5 = SUMPRODUCT(B5:C5,B6:C6)
D8 = SUM(B8:C8)
D9 = SUM(B9:C9)
D10 = SUM(B10:C10)

B11 = 0.2 * SUM(B5:C5)
B12 = 0.3 * SUM(B5:C5)

c.
Maximum Revenue: $220289.855
Amount of coutry tables: 405.797101
Recommend amount of country tables: 405
Amount of contemporary tables: 173.913043
Recommend amount of contemporary tables: 174

Looking at the results, we can see that we are trying to maximize the production of country table while staying within the bound of the constraints. Producing 406 country tables and 173 contemporary tables will exceed the constraint of the sander machine. So we recommanded production output to be 405 for country table and 174 for contemporary table in order to respect all contraints. The final revenue given this output will be $220050.



