5. Find the current $I_1$ in Fig. 5. (5%)

6. Find the current \( I_1 \) and \( I_2 \) in Fig. 6. (10%)

7. Find the current \( I_1 \) pass through the \( 8\Omega \) resistor and the short-circuit current \( I_2 \) in Fig. 7. (15%, 5% for \( I_1 \) and 10% for \( I_2 \))

8. The wire is 10m long with 5A current passing through. The directions of the magnetic fields are shown in Fig. 8a and 8b. Their magnetic flux densities are both $1Wb/m^2$. Find the two magnetic forces on the current-carrying wires in Fig. 8a and 8b. (10%)

9. In Fig. 9, ε=100V, R1=10Ω, R2=20Ω, R3=30Ω, and L=2H. Immediately after switch S is closed, what are (a) i₁ and (b) i₂? A long time later, what are (c) i₁ and (d) i₂? The switch S is then reopened. Just then, what are (e) i₁ and (f) i₂? A long time later, what are (g) i₁ and (h) i₂? (16%)

10. For the magnetic circuit of Fig. 10, the current \( i \) flows through the coil of \( N \) turns. The mean core length is \( \ell_c \), and the air gap length is \( \ell_g \). Assume no magnetic leakage. The flux crossing the cross-sectional area \( A \). The relative permeability of core is \( \mu_r \). The permeability of air is \( \mu_0 \). Find the flux in the air gap. (10%)

(1) A company is looking to purchase and replace a fixed asset for $2,100,000. It will sell the asset that will be replaced for $410,000 but will incur a $10,000 gain upon that sale. It must also commit $300,000 of working-capital to the investment. The firm's tax rate is 20%. Required: What is the amount of the relevant initial investment?

(2) The NTPU Company orders most of its items in lot sizes of 10 units. Average annual demand per side of beef is 720 units per year. Ordering costs are $25 per order with an average purchasing price of $100. Annual inventory carrying costs are estimated to be 40% of the unit cost. Required: Determine the annual cost savings if NTPU Company changes its order size from 10 units to the economic order quantity.

(3) NTPU Corporation makes miniature statues of the Empire State Building from cast iron. Sales total 50,000 units a year. The statues are finished either rough or polished, with an average demand of 60% rough and 40% polished. Iron ingots, the direct material, costs $5 per pound. Processing costs are $300 to convert 30 pounds into 60 statues. Rough statues are sold for $17 each, and polished statues can be sold for $19 or engraved for an additional cost of $5. Polished statues can then be sold for $40. Required: Determine whether NTPU Company should sell the engraved statutes. Why?

(4) NTPU Corp is committed to its quality program. It works with all areas of the company to establish sound quality programs within reasonable budget guidelines. For 2026, it has budgeted $1,000,000 for prevention costs and $900,000 for appraisal costs. Internal failure has a budget of $100 per failed item, while external failure has a total budget of $600,000. Product Testing has proposed to management a change in the 2026 budget for a new method of testing products. If management decides to implement the new method, $1.5 per unit of appraisal costs will be saved, up to a level of 150,000 tests. No additional savings are expected past the 150,000 level. The new method involves $95,000 in training costs and $65,000 in yearly testing supplies. Traditionally, 5% of all completed items have to be reworked. External failure costs average $120 per failed unit. The company's average external failures are 1% of units sold. The company carries no ending inventories. Required: How much do internal failure costs change, assuming 500,000 units are tested under the new method and it reduces the amount of unacceptable units in the manufacturing process by 40%?

(5) LUKE is considering purchasing a new computer network for $82,000. It will require additional working capital of $13,000. Its anticipated eight-year life will generate additional client revenue of $33,000 annually with operating costs, excluding depreciation, of $15,000. At the end of eight years, it will have a salvage value of $9,500 and return $5,000 in working capital. Taxes are not considered. The company has a required rate of return of 14%. Required: What is the net present value of the proposed investment? What is the internal rate of return?

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