Tom and Jerry Associates estimates that the number of handcrafts they sell in a

Question

Tom and Jerry Associates estimates that the number of handcrafts they sell in a year is a function of TV and Radio advertising expenditure. The function expressing this relationship is given as;
Z = 2000X + 5000Y – 20X2 – 10Y2 – 50XY
Where, X = the amount spent on TV advertisement, and Y = amount spent on Radio advertisement (the expenditures are expressed in thousands of shillings)
After considering budgetary constraints, the firm allocates a total advertisement budget of Ksh 80,000. What is the optimal level of sales for Tom and Jerry Advocates?

Explanation / Answer

The number of handcrafts Z sold in a year is a function of TV expenditure X (thousands of shillings) and Radio advertising expenditure Y (thousands of shillings)

Z = 2000X + 5000Y – 20X2 – 10Y2 – 50XY

After considering budgetary constraints, the firm allocates a total advertisement budget of Ksh 80,000. This implies X + Y = 80,000. Hence we need to maximize Z such that X + Y < or = 80,000

Using excel solver, the results are X = 0 and Y = 80. This will maximize the number to 336000.

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