Jan's Dry Cleaning holds $10,000 on a typical day, although only $2,000 is essential for carrying out business. Making a midday deposit is estimated to reduce cash holdings to $8,000 and cost an extra $80 per year in lost production. If, in addition, an armored car service is engaged to pick up cash more frequently for a fee of $120 per year, cash holdings will be further reduced to $6,000 per day. Employing a computerized cash management service for an annual fee of $180 would reduce cash holdings further to $4,000. If any reduction in cash holdings will be invested in government bonds earning 3 percent, then how much money should Jan's hold?

$6000

Explanation:

If holding is $10000,

Reduction in cash holding = (10000-10000) = 0  

Interest earned in government bonds=(Reduction in holdings) × 0.03 =0

Cost of deposits = 0

Additional benefit = (interest earned - cost of deposit)

Additional benefit = 0-0 = 0

Making a mid day deposit;

Reduction in cash holding = (10000-8000) = $2000

Interest earned in government bonds = Reduction in holdings × 0.03

= 2000 × 0.03 =$60

Cost of deposits=$80

Additional benefit=$60-80=-$20

Using a armored car service;

Reduction in cash holding=(10000-6000)=4000

Interest earned in government bonds= 4000 × 0.03 = $120

Cost of deposits=$120

Additional benefit=120 - 120= $0

Using computerized cash management service;

Reduction in cash holding=(10000-4000)=6000

Interest earned in government bonds;

6000 × 0.03 = $180

Cost of deposits=$180

Additional benefit=180 - 180=$0

Additional benefit is maximized in case of both computerized management service and armor vehicle . So, Optimal cash holding is $6000