Production of Jack\'s best-selling Squeaky Toy follows this model: C(x) = 0.5 x^

Question

Production of Jack's best-selling Squeaky Toy follows this model: C(x) = 0.5 x^2 - 5x + 20 Where x is the number of toys and C is the monthly cost to produce the toys. How many toys should be produced monthly to minimize Average Cost? What is the Average Cost at the above toy production (the minimum) Write UNITS for this The number of portable CD players you are prepared to supply to a retail outlet every week is given by the formula q = 0.4 p^2 + 2p where p is the price it offers you. The retail outlet is currently offering you $50 per CD player. If the price it offers decreases at a rate of $3 per week, how will this affect the number you supply?

Explanation / Answer

3. C(x)= 0.5x^2 - 5x+20

This equation represents a quadratic equation and the cost is minimum at its vertex.

The formula of vertex,x = -b/2a= -(-5)/2(0.5)=5

Therefore 5 toys should be produced monthly to minimize the average cost.

b) Average cost at minimum number of toys,C(5)=0.5(5)^2 -5(5)+20= 12.5-25+20= 7.5

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