93年 - 93 國立暨南大學轉學生招生考試試題_經濟系：微積分#124693

(a) What level of production will produce a maximum profit?

(b) What level of production will produce a minimum average cost per unit?

(a)

(b)

3.A corporation manufactures a product at two locations. The cost functions for producing x₁ units at location 1 and x₂ units at location 2 are C₁=0.05x₁²+15x₁+5400 and C₂=0.03x₂²+15x₂+6100 respectively. The demand function for the product is p=225-0.4(x₁+x₂). Find the production levels at the two locations that will maximize the profit.

4. A company produces a new product for which it estimates the annual sales to be 8000 units. Suppose that in any given year 10% of the units (regardless of age) will become inoperative. Find the market stabilization level of the product.

(a)

(b)

(c)

6. You are in a pond 2 km from the nearest point on the coast. You are to go to point A, 3 km down the coast and 1 km inland (see figure). You can swim at a rate of 2 km per hour and you can walk at a rate of 4 km per hour. Toward which point on the coast should you swim in order to reach point A in the shortest time?