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$$.\begin{aligned}.& S(P)=\frac{1}{2} P+40 \\.& D(P)=220-P.\end{aligned}.$$.The quantity of a product supplied and the quantity of the product demanded in an economic market are functions of the price of the product. The functions above are the estimated supply and demand functions for a certain product. The function $S(P)$ gives the quantity of the product supplied to the market when the price is $P$ dollars, and the function $D(P)$ gives the quantity of the product demanded by the market when the price is $P$ dollars. How will the quantity of the product supplied to the market change if the price of the product is increased by $\$ 10$ ?

SAT · Math · previous-year question

  1. A.The quantity supplied will decrease by 5 units.
  2. B.The quantity supplied will increase by 5 units.correct
  3. C.The quantity supplied will increase by 10 units.
  4. D.The quantity supplied will increase by 50 units.

Answer

B. The quantity supplied will increase by 5 units.

Explanation

Choice $\mathbf{B}$ is correct. The quantity of the product supplied to the market is given by the function $S(P)=\frac{1}{2} P+40$. If the price $P$ of the product increases by $\$ 10$, the effect on the quantity of the product supplied can be determined by substituting $P+10$ for $P$ in the function $S(P)=\frac{1}{2} P+40$. This gives $S(P+10)=\frac{1}{2}(P+10)+40=\frac{1}{2} P+45$, which shows that $S(P+10)=S(P)+5$. Therefore, the quantity supplied to the market will increase by 5 units when the price of the product is increased by $\$ 10$.Alternatively, look at the coefficient of $P$ in th

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