Midwest Healthcare is a managed care plan submitting a premium bid to Vandelay Industries, a large manufacturer in its service area. The premium bid includes primary care for all Vandelay employees. Vandelay has provided information about the age and gender of its employees, and Midwest Healthcare has identified average primary care utilization rates from its databases. This information is shown below:

Vandelay Industries

Average primary care

Age band

Number of Males

Number of Females

Visits per year $-$ Males

Visits per year $-$ Females

$20-29$

$310$

$330$

$2\mathrm{.}25$

$3\mathrm{.}35$

$30-39$

$101$

$140$

$2\mathrm{.}75$

$3\mathrm{.}65$

$40-49$

$56$

$60$

$3\mathrm{.}30$

$4\mathrm{.}10$

$50-59$

$46$

$36$

$4\mathrm{.}25$

$4\mathrm{.}75$

$60+$

$9$

$12$

$5\mathrm{.}10$

$5\mathrm{.}20$

Primary care physicians can each handle about $2,750$ patient visits per year, for which they are paid $$200,000.$

What primary care rate $($PMPM$)$ will Midwest Healthcare propose to Vandelay Industries?