The following is a production possibilities model. Use the equation to compute various levels of y for given x's. Note that as we produce more x, we have to reduce production of y. Next plot the curve.

y:=-0.25*x^2-0.50*x +42;

> eval(y,x=10);

> eval(y,x=5);

> eval(y,x=9);

> eval(y,x=8);

> plot( -0.25*x^2-0.50*x +42, x=0..13);

> eval(y,x=10);

> qd:=3-p^2;

qd := 3-p^2

>

> qs:=6*p-4;

WHAT IS THE EQUILBRIUM PRICE AND QUANTITY?

> plot({3-p^2,6*p-4},p=0..2);

> eval(qd,p=1);

> eval(qs,p=1);

> qd:=8-p^2;

> qs:=p^2-2;

WHAT IS THE EQUILBRIUM PRICE AND QUANTITY?

> plot({8-p^2,p^2-2},p=0..3);

> solve(8.0-p^2=p^2-2.0,p);

> eval(qd,p=2.236067978);

> qdb:=10-2*pb+pc;

qdb := 10-2*pb+pc

> qsb:=-2 +3*pb;

qsb := -2+3*pb

> qdc:=15 +pb-pc;

qdc := 15+pb-pc

> qsc:=-1 +2*pc;

qsc := -1+2*pc

WHAT IS THE EQUILBRIUM PRICE AND QUANTITY FOR BOTH BEEF AND CHICKEN?.pb=price of beef,

pc=price of chicke,. Both markets must be in equilibrium; that is qdb must equal qsb, and qdc=qsc. Putting all this information together, we solve for pc and pb in the following.

> solve({10-2*pb+pc=-2.0 +3*pb,15 +pb-pc=-1.0 +2*pc},{pb,pc});

>

>

> eval(qsc, {pc= 6.571428571,pb= 3.714285714});

>

> eval(qsb,{pc= 6.571428571,pb= 3.714285714});

9.14285714

> eval(qdb,{pc= 6.571428571,pb= 3.714285714});

9.142857143

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