Answer:
812.40 units
Explanation:
Given that,
Annual holding cost percentage = 20%
Ordering cost = $110 per order
Annual demand = 15,000 units
Units Ordered - Price Per Unit
1-250 - $30.00
251-500 - $28.00
501-750 - $26.00
751 and up - $25.00
Optimal order quantity:
= 
= 
= 
= 812.40
Therefore, the optimal order quantity is 812.40 units.
Answer:
Objective function:
Maximize Z: 30P1 + 25P2 + 28P3
Subject to: 2.00P1 + 1.50P2 + 3.00P3 ≤ 450 (Department A constraint)
2.50P1 + 2.00P2 + P3 ≤ 350 (Department B constraint)
0.25P1 + 0.25P2 + 0.25P3 ≤ 50 (Department C constraint)
P1, P2, P3 ≥ 0 (Non-negativity)
Explanation:
The objective function is formulated from the contribution margin of the three products. For instance, the contribution of Product 1 is $30, the contribution of Product 2 is $25 and the contribution of Product 3 is $28. Thus, the objective function will be 30P1 + 25P2 + 28P3.
The constraints were obtained from the departmental labour hours requirements for each product. For instance, Product 1 requires 2 hours in department A, Product 2 requires 1.50 hours in department A and Product 3 requires 3 hours in Department A. Thus, the constraint will be 2.00P1 + 1.50P2 + 3.00P3.
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Answer:
Mark should invest:
- $30,000 in short term bonds
- $30,000 in intermediate term bonds
- $40,000 in long term bonds
Explanation:
S = short term bonds
I = intermediate term bonds
L = long term bonds
S + I + L = 100,000
0.04S + 0.06I + 0.07L = 0.058 x 100,000 = 5,800
S = I
2S + L = 100,000
L = 100,000 - 2S (now we replace both I and L)
0.04S + 0.06s + 0.07(100,000 - 2S) = 5,800
0.1S + 7,000 - 0.14S = 5,800
7,000 - 5,800 = 0.14S - 0.1S
1,200 = 0.04S
S = 1,200 / 0.04 = 30,000
I = 30,000
L = 100,000 - 60,000 = 40,000
