阿皮 asked in 科學數學 · 8 years ago

投資決策分析題目

A company produces and sells a comsumer product and is able to contral the demand for the product by varying the selling price.The approximate relationship between price and demand is

p=$40+(3800/D)-(6000/D^2) , for D>1 ,

where p is the price per unit in dollars and D is the demand per month .The company is seeking to maximize its profit.The fixed cost is $1500 per month and the variable cost(cv) is $42 per unit.

(1)What is the number of units that should be produced and sold each month to maximize profit?

(2) Show that your answer to part(1) maximize profit.

很急><

拜託大家解一下...

1 Answer

Rating
  • 小白
    Lv 7
    8 years ago
    Favorite Answer

    價格 p = 40 + 3800/D - 6000/D^2

     

    數量 = D

     

    因此,營業額 = D × p = 40D + 3800 - 6000/D

     

    總成本 = 1500 + 42D

     

    利潤 = 營業額 - 總成本 = 40D + 3800 - 6000/D - 1500 - 42D = 2300 - (2D + 6000/D)

     

    算術平均大於等於幾何平均 ==> 2D + 6000/D ≥ 2 × √(2D × 6000/D) = 219

     

    因此,利潤 ≤ 2081

     

    此時,2D = 6000/D ==> D = 54 或 55

     

    D = 54,利潤 = 2081

     

    D = 55,利潤 = 2081

     

    生產 54 或 55 個,可達最大利潤。

     

     

    • Login to reply the answers
Still have questions? Get your answers by asking now.