The Little Theatre had tentatively planned to put on six different productions with a total of $108$ performances. For

example, one of the productions was Peter Rabbit, which had a six$-$week run with three performances on each

weekend. The costs from the current year's planning budget appear below.

The Little Theatre

Costs from the Planning Budget

For the Year Ended December $31$

Some of the costs vary with the number of productions, some with the number of performances, and some are fixed

and depend on neither the number of productions nor the number of performances. The costs of scenery, costumes,

props, and publicity vary with the number of productions. It doesn't make any difference how many times Peter Rabbit

is performed, the cost of the scenery is the same. Likewise, the cost of publicizing a play with posters and radio

commercials is the same whether there are $10,20,$ or $30$ performances of the play. On the other hand, the wages of

the actors, directors, stagehands, ticket booth personnel, and ushers vary with the number of performances. The

greater the number of performances, the higher the wage costs will be$.$ Similarly, the costs of renting the hall and

printing the programs will vary with the number of performances. Administrative expenses are more difficult to

analyze, but the best estimate is that approximately $75\%$ of the budgeted costs are fixed, $15\%$ depend on the number

of productions staged, and the remaining $10\%$ depend on the number of performances.

After the beginning of the year, the board of directors of the theater authorized expanding the theater's program to

seven productions and a total of $168$ performances. Not surprisingly, actual costs were considerably higher than the

costs from the planning budget. $($Grants from donors and ticket sales were also correspondingly biahof are not

shown here.$)$ Data concerning the actual costs were as follows: