Howard's Apple Farm makes applesauce and apple juice from their apples. It costs $$0\mathrm{.}80$ to produce a jar of applesauce and $$0\mathrm{.}60$ to produce a bottle of apple juice The farm has a policy that at least $20\%$ but not more tha $60\%$ of its output must be applesauce. The farm wants $t$ meet but not exceed the demand for each product. Howard estimates that the demand for applesauce is normally $5,000$ jars, plus an additional $3$ jars for each $$1$ spent on advertising for applesauce. The normal demand for apple juice is estimated to be $4,000$ bottles, plus an additional $5$ bottles for every $$1$ spent on advertising for apple juice. The farm has $$16\mathrm{.}000$ to spend on producing and advertising its two products. Applesauce sells for $$1\mathrm{.}75$ per jar; apple juice sells for $$1\mathrm{.}75$ per bottle. Howard wants to know how many units of each product to produce, and how much advertising to spend on each product, in order to maximize profit. Can you help him?