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.

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 higher, but are not shown here.$)$ Data concerning the actual costs

appear below: