23.pdf - Supply/Demand/Revenue/Cost/Profit 1 Given S(q = 0.75q and D(q = 60 – 0.75q a Find the Equilibrium Point(40,30 b Graph the Supply and Demand

# 23.pdf - Supply/Demand/Revenue/Cost/Profit 1 Given S(q =...

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Supply/Demand/Revenue/Cost/Profit 1. Given: S(q) = 0.75q and D(q) = 60 0.75q a) Find the Equilibrium Point. (40,30) b) Graph the Supply and Demand functions. c) Label Surplus and Shortage on the graph. 2. Given: ?(𝑥) = 𝑥 2 + 10𝑥 and ?(𝑥) = 900 − 20𝑥 − 𝑥 2 a) Find the Equilibrium Point. (15,375) b) Graph the Supply and demand functions. 3. Given: D(p) = -4p + 28 a) Find the Demand in terms of quantity. P = D(q) = (-1/4)q + 7 b) Find the Revenue in terms of quantity. ?(?) = (− 1 4 ) ? 2 + 7? c) Find the Revenue in terms of price. ?(?) = −4? 2 + 28? 4. Given: D(x) = 1000 50x a) Find the Demand in terms of price. x = D(p) = (-1/50)p + 20 b) Find the Revenue in terms of price. ?(?) = (− 1 50 ) ? 2 + 20? c) Find the Revenue in terms of quantity. ?(𝑥) = 1000𝑥 − 50𝑥 2 5. Eighty apartments rent for \$200 each. For each increase of \$20, one apartment becomes vacant. a) Write the Revenue function R(v), if v is the number of vacant apartments. ?(𝑣) = 16000 + 1400𝑣 − 20𝑣 2 b) Write the Revenue function R(a), if a is the number of apartments rented. ?(𝑎) = 1800𝑎 − 20𝑎 Subscribe to view the full document. Unformatted text preview: 2 c) Determine the number of vacant apartments that will maximize revenue. 35 vacant apartments d) Determine the number of apartments that will maximize revenue. 45 apartments e) Determine the maximum revenue. \$40,500 6. An item sells for \$50 per unit. It costs \$4 per unit to produce plus a fixed cost of \$500. a) Determine the Revenue Function. R(x) = 50x b) Determine the Cost Function. C(x) = 4x + 500 c) Determine the Break-Even Point. (250/23,12500/23) d) Graph the Revenue and Cost Functions. e) Label Profit and Loss on the graph. f) Determine the Profit Function. P(x) = 46x - 500 7. Given: ?() = 2 + 5000 and ?() = 10 − 2 1000 a) Determine the Break-Even Point(s). (683,6367) and (7317, 19633) values in points are approximate b) Graph the Revenue and Cost Functions c) Label Profit and Loss on the graph. b) Determine the Profit Function. () = (− 2 1000 ) + 8 − 5000 c) Determine the number of units that will maximize profit. 4000 units d) Determine the maximum profit. \$11,000...
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