LSP pellets were made by the secret process of mixing LSD with opium in the optimum proportion of $8$:$2$ and converting the mixture into pellets. Though there was no expected loss in mixing, the pellet$-$making process normally resulted in a loss of $10$ percent of the total input.

The Joint was run by four enterprising young men: Arora $$ in$-$charge of purchasing, Bansal $$ in$-$charge of mixing, Cabral $$ specializing in making the pellets out of the mixed material, and D'Souza $$ in$-$charge of selling.

In June, Arora bought enough raw materials to make $270$ units of LSP as agreed upon by the group in advance, but D'Souza owing to heavy involvement in other personal activities could book orders only for $216$ units of LSP$.$ Bansal from his long experience in the line knew that the shelf life for LSP is very short compared to LSD or opium and prepared enough mixture for $216$ units of LSP$.$ Cabral who got enough mixture to make $216$ units of LSP ended up making only $207$ finished units with not a trace of the mixture leftover. He was so dazed that he could not even explain how he produced less than what he was supposed to$.$

Total consumption of raw materials for June was as follows:

$$ LSD $200$ units, all from units bought in June @ $$11/$unit$.$

$$ Opium $40$ units, all from units bought in June @ $$4\mathrm{.}50/$unit$.$

Materials cost was their only cash cost, though they all thought that their time was worth $$10/-$ per hour. In fact, all of them had enough free time to spare for the joint.

Investigations showed that Arora had paid a premium of $10$ percent on the standard price for LSD as he got carried away by a cute little tourist from whom he bought it$.$ When he came to his senses$,$ he realized his folly and tried to make for it by getting a $10$ percent discount on the standard price of opium. When Cabral came to know that Arora paid a lower price for opium, he $($Cabral$)$ claimed that his pellet making got fouled up because of the 'lower quality' opium. Interestingly he never gave this explanation until he knew about the actual price paid for the raw materials.

Though D$$Souza claimed earlier that he sold less units than the budgeted $240$ units, as he had to go to Calcutta on a private trip, investigations showed that he had lost sales because he jacked up the price by $10$ percent on the standard price of Rs$\mathrm{.}40$ per unit of LSP$.$ He did, however, bring in the revenue to the Joint$$s account at the higher realization per unit.

You can make necessary assumptions where required.

Required:

$1.$Calculate for sales the variances: $($a$)$ total sales variance, $($b$)$ sales price variance, and $($c$)$ sales quantity variance.

$2.$Calculate $($a$)$ total material cost variance, $($b$)$ material price variance, and $($c$)$ material quantity variance.

$3.$Breakdown the sales quantity variance into $($a$)$ sales budget revision variance, and $($b$)$ sales activity or capacity variance.

$4.$Breakdown the material quantity variance into $($a$)$ material budget revision variance, material activity variance, $($c$)$ material yield or wastage variance, and $($d$)$ material mix variance.

$5.$Calculate profit variance $($difference between the budgeted profits and actual profits$).$

$6.$Who has contributed in loss of profits and how much? You may attempt to determine the responsibility of each individual in terms of contribution in gain or loss of profits.

$7.$Do you think your answer to question $6$ above can be justified in fixing the responsibility? What are the difficulties that one would face while using the variances for fixing responsibilities for departments or people in the organization?