# After paying its monthly bills, a family has \$100 left over to spend on leisure. The family…

After paying its monthly bills, a family has \$100 left over to spend on leisure. The family enjoys two types of activities: (i) eating out; and (ii) other entertainment, such as seeing movies and sporting events. The family has determined the relative value (utility) of these two activities—each dollar spend on eating out provides 1.2 units of value for each dollar spent on other entertainment. Suppose that the family wishes to determine how to spend this money to maximize the value of its expenditures, but that no more than \$70 can be spent on eating out and no more than \$50 on other entertainment (if desired, part of the money can be saved). The family also would like to know:

a) How the total value of its expenditures for leisure would change if there were only \$99 to spend.

b) How the total value would change if \$75 could be spend on eating out.

c) Whether it would save any money if each dollar of savings would provide 1.1 units of value for each dollar spent on other entertainment

Formulate the family’s spending decision as a linear program. Sketch the feasible region, and answer each of the above questions graphically. Then solve the linear program by the simplex method, identify shadow prices on the constraints, and answer each of these questions, using the shadow prices.

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