You work as the production line manager for Dan's Cat Empurrium, purveyor of all things cat related. You have to decide what product mix to produce to stock the grand opening of a Bothell storefront. 

Your factory can produce cat hats, kitten mittens, a special Dan cat toy, cat food and kitty litter. The storefront manager has requested you stock at least 150 of each product. Cat hats sell for $10 each, kitten mittens for $8 each, the special cat toy $4 each, cat food $16 per bag and kitty litter for $14. Cat hats use $2.50 worth of cotton and kitten mittens use $3 worth of cotton to produce. The special cat toy uses $1 of cotton and $0.50 of clay to produce. Cat food is directly imported from the Blue Buffalo company for $12 a bag. Kitty litter uses $5 worth of clay to produce.

Your storeroom currently holds $2500 worth of cotton and $1500 worth of clay. Your contract for Blue Buffalo states that they will provide batches of 50 bags of cat food, up to maximum of 400 bags.

Finally, your storefront manager has informed you that they can only stock a total of 1200 accessories (cat hats, kitten mittens and cat toys) and only a total of 850 essentials (cat food and kitty litter).

Determine the optimal product mix to maximize profit and make sure to save the Sensitivity report. Report the max profit rounded to the nearest dollar.