所屬科目:研究所、轉學考(插大)-微積分
(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.
(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?