Number and Algebra
Functions
Geometry and Trigonometry
Statistics and Probability
Calculus
A company sells a product at a fixed price of 181818 per unit and has cost function C(q)=5q2−22q+200C(q)=5q^2-22q+200C(q)=5q2−22q+200. Determine the quantity qqq that maximizes profit.
A firm faces a linear demand p(q)=100−2qp(q)=100-2qp(q)=100−2q and incurs cost C(q)=20q+50C(q)=20q+50C(q)=20q+50. Find the output level qqq that maximizes profit.
A bakery sells cakes at p(q)=60−0.5qp(q)=60-0.5qp(q)=60−0.5q dollars each and has cost C(q)=10q+150C(q)=10q+150C(q)=10q+150. Find the production level qqq that maximizes profit.
A smartphone maker earns 300300300 dollars per unit and has cost function C(q)=0.5q2+50q+1000C(q)=0.5q^2+50q+1000C(q)=0.5q2+50q+1000. Determine the output qqq that maximizes profit.
A service provider has profit function P(q)=70q−0.005q2−200P(q)=70q-0.005q^2-200P(q)=70q−0.005q2−200. Find the value of qqq that maximizes profit.
The price-demand function is p(q)=80−0.1qp(q)=80-0.1qp(q)=80−0.1q and the cost function is C(q)=2q+300C(q)=2q+300C(q)=2q+300. Determine qqq that maximizes profit.
Revenue is R(q)=40q−0.5q2R(q)=40q-0.5q^2R(q)=40q−0.5q2 and cost is C(q)=5q+100C(q)=5q+100C(q)=5q+100. Find qqq that maximizes profit.
Total revenue is R(q)=120q−0.2q2R(q)=120q-0.2q^2R(q)=120q−0.2q2 and cost is C(q)=30q+400C(q)=30q+400C(q)=30q+400. Determine the output level q≥0q\ge0q≥0 that maximizes profit.
The total cost of producing qqq units is given by C(q)=q3−30q2+300q+200C(q)=q^3-30q^2+300q+200C(q)=q3−30q2+300q+200. Determine the output qqq that minimizes cost.
A car manufacturer faces demand p(q)=50000−0.01qp(q)=50000-0.01qp(q)=50000−0.01q and cost C(q)=20000q+106C(q)=20000q+10^6C(q)=20000q+106. Find the output qqq that maximizes profit.
A product’s price depends on demand: p(q)=200−qp(q)=200-qp(q)=200−q, and its cost is C(q)=0.01q2+2q+500C(q)=0.01q^2+2q+500C(q)=0.01q2+2q+500. Determine the output level qqq maximizing profit.
A company’s revenue is R(q)=150ln(q)R(q)=150\ln(q)R(q)=150ln(q) and cost is C(q)=20q+100C(q)=20q+100C(q)=20q+100. Find the output qqq that maximizes profit.
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