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MAT284-2006Fall

# MAT284-2006Fall - p = 75 6(a Find the marginal cost when q...

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MAT 284 Final fall 2006 Name: 1. A refrigerator manufacturer will produce 3100 units when the price is \$850 and 2100 units when the price is \$750. Assuming that price and quantity are linearly related find the supply equation. 2. The manufacturer of Super Duper sports energy gel will break even at total sales of \$500,000. If fixed costs are \$40,000 and each gel pack sells for \$1.25 determine the variable costs per unit. 3. Solve for x , log(( x - 5)( x - 20)) = 2.

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4. Find all points on the curve y = e x + 1 where the tangent line has slope 1. 5. Given the cost function c = 7500 + 12 q + 0 . 2 q 2 and quantity as a function of price q = 900 - 2 p find the rate of change of cost with respect to price when
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Unformatted text preview: p = 75. 6. (a) Find the marginal cost when q = 10 given the average cost ¯ c = 0 . 0002 q 4-. 01 q 2 + 6 + 20000 /q . (b) What does your answer mean? 7. Given that marginal cost is dc dq = 0 . 12 q 2-2 . 4 q + 9 and ﬁxed cost are 9700 ﬁnd the total cost when q = 10. 8. Given the demand q = p 2500-p 2 ﬁnd the point elasticity of demand when p = 30. If the price of 30 decreases 4 5 % what is the approximate change in demand? 9. Sketch the graph, this includes ﬁnding the intervals of increase, decrease, concave up, concave down, local extrema and inﬂection points. y = 3 x ( x-2) 2 ....
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