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10 Nov 2019
1.
The number of units x that consumers are willing to purchase at a given price p is defined as the demand function p=f(x). Suppose the cost of production is given by C(x)=4000- 40x + 0.02x2 and the demand function is p(x)= 50 -x/100. Find the unit price p that produces maximum profit. Find the number of items x for which production cost is minimum. Find the value of x for which average cost C- per item is minimum. (Hint: C- is minimum where its graph has a horizontal tangent line, so the derivative of C- is zero) When average cost C- is minimum, show that average cost and marginal cost are equal. Having produced 1000 items, approximate the additional cost of producing one more. Do the same for 5000 items.
1.
The number of units x that consumers are willing to purchase at a given price p is defined as the demand function p=f(x). Suppose the cost of production is given by C(x)=4000- 40x + 0.02x2 and the demand function is p(x)= 50 -x/100. Find the unit price p that produces maximum profit. Find the number of items x for which production cost is minimum. Find the value of x for which average cost C- per item is minimum. (Hint: C- is minimum where its graph has a horizontal tangent line, so the derivative of C- is zero) When average cost C- is minimum, show that average cost and marginal cost are equal. Having produced 1000 items, approximate the additional cost of producing one more. Do the same for 5000 items.
Nelly StrackeLv2
13 Jan 2019