Suppose that sales representatives sell one particular Sony high-definition TV m

Question

Suppose that sales representatives sell one particular Sony high-definition TV model. Let q represent the number of TVs sold per day, s the number of skilled sales reps per day, and u the number of unskilled reps per day. Working eight hours per day, each skilled worker sells 8 TVs per day and each unskilled worker sells 1. The wage rate of the skilled workers is ws=$176.00 per eight-hour day, and the wage rate of the unskilled workers is wu=$29.33 per day.

Identify the cost-minimizing number of skilled and unskilled sales representatives to sell q=16 TVs per day.

Explanation / Answer

q = 16

s = the number of skilled sales reps per day, and

u = the number of unskilled reps per day.

16 = 8s + u

Cost of sales rep

176*s + 29.33*u

So , Putting lagrange function to minmize cost given 16 = 8s + u

L = 176*s + 29.33*u + (16 - 8s - u)

dL/ds = 176 - 8

dL/du = 29.33 -

dL/d = 16 - 8s - u

Putting dL/ds =dL/du = dL/d = 0 and solving for s and u

s = 2 and u = 4

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