Formulate and then solve a linear programming model of this problem, to determine how many containers of each product to produce tomorrow to maximize profits. The company makes four juice products using orange, grapefruit, and pineapple juice.

Product	Retail Price per Quart
Orange juice	$1.00
Grapefruit juice	.90
Pineapple juice	.80
All-in-One	1.10

The All-in-One juice has equal parts of orange, grapefruit, and pineapple juice. Each product is produced in a one-quart size (there are four quarts in a gallon). On hand are 400 gallons of orange juice, 300 gallons of grapefruit juice, and 200 gallons of pineapple juice. The cost per gallon is $2.00 for orange juice, $1.60 for grapefruit juice, and $1.40 for pineapple juice. In addition, the manager wants the Grapefruit Juice product to comprise no more than 30 percent of the total number of containers produced. She wants the ratio of the number of containers of orange juice to the number of containers of pineapple juice to be at least 7 to 5. (Do not round intermediate calculations. Round your final answers to nearest whole number. Leave no cells blank - be certain to enter "0" wherever required.)

Additionally, what is the optimal value of the onjective function coefficient z?