If a contractor\'s price for an aircraft component is p dollars per unit, then t

Question

If a contractor's price for an aircraft component is p dollars per unit, then the military will purchase q hundred units according to the demand equation p2 + q = 101 When the military price is p dollars per unit, the contractor is willing to supply q hundred units according to the supply equation 2p -q = 16. Equilibrium price is the price at which quantity supplied equals quantity demanded. Determine the equilibrium price. Determine the number of units that will be supplied at the equilibrium price.

Explanation / Answer

p^2 + q = 104 2p - q = 16 You are going to solve by the substitution method. Solve for q from the second equation, so you get: q = 2p - 16 Plug it into the first equation: p^2 + 2p - 16 = 104 Subtract 104 from both sides p^2 + 2p - 120 = 0 Now you can either use quadratic formula to solve or factor out: (p + 12)(p - 10) = 0 Solving for p you get p=-12 and p=10, but you know it can't be -12 because price can't be negative, so you have p = 10. To solve for the number of units just plug in p = 10 to either one of your equations and solve for q. 2(10) - q = 16 20 - q = 16 q = 4

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