The Little Theatre is a nonprofit organization devoted to staging plays for children. The theater has a very small full$-$time professional administrative staff. Through a special arrangement with the actors' union, actors and directors rehearse without pay and are paid only for actual performances, 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 $31$

budgeted number of productions $...6$

Budgeted number of performances $...108$

Actors and directors$$ wages $216,000$

Stagehands wages $......32,400$

Ticket booth personnel and ushers wages $16,200$

Scenery, costumes, and props $..........................108,000$

Theater hall rent $.....................................54,000$

Printed programs $27,000$

Publicity $........12,000$

Administrative expenses $43,200$

Total $ $508,800$

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 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 were as follows:

The Little Theatre

Actual Costs

for the Year Ended December $31$

Actual number of productions $7$

Actual number of performances $168$

Actors and directors$$ wages $$341,800$

Stagehands wages $49,700$

Ticket booth personnel and ushers$$ wages $25,900$

Scenery, costumes, and props $130,600$

Theater hall rent $78,000$

Printed programs $38,300$

Publicity $15,100$

Administrative expenses