SQL Schema Level Constraint - mysql

Question

I've got a constraint between some tables I'm trying to implement, I imagine I should be doing it on the db level, but I'm struggling to come up with the right terms to google, maybe you guys can help!
If I have the tables:
Product [coke, banana, chocolate etc]
ProductType [food, drink, cosmetics etc]
Location [fridge, shelf, cupboard etc]
If -> is many-to-one, and >-< is many-to-many
Product -> ProductType
Product -> Location
ProductType >-< Location
Given a fridge, we know a fridge can contain [food,drink], so on the application level, we present the user with only the food and drink products to allocate to fridge. Is there a way on the db level to ensure that fridge only contains products from its permitted types?
Below is the SQL code I came up with for the above, in the last part I insert 'coke', with ProductType 'drink'. How to I make sure it therefore can't be put in a 'cupboard'
CREATE SCHEMA IF NOT EXISTS `test` DEFAULT CHARACTER SET utf8 COLLATE utf8_general_ci ;
USE `test` ;
-- -----------------------------------------------------
-- Table `test`.`Location`
-- -----------------------------------------------------
CREATE TABLE IF NOT EXISTS `test`.`Location` (
`id` INT NOT NULL AUTO_INCREMENT,
`name` VARCHAR(45) NULL,
PRIMARY KEY (`id`))
ENGINE = InnoDB;
-- -----------------------------------------------------
-- Table `test`.`ProductType`
-- -----------------------------------------------------
CREATE TABLE IF NOT EXISTS `test`.`ProductType` (
`id` INT NOT NULL AUTO_INCREMENT,
`name` VARCHAR(45) NULL,
PRIMARY KEY (`id`))
ENGINE = InnoDB;
-- -----------------------------------------------------
-- Table `test`.`Product`
-- -----------------------------------------------------
CREATE TABLE IF NOT EXISTS `test`.`Product` (
`id` INT NOT NULL AUTO_INCREMENT,
`name` VARCHAR(45) NULL,
`Location_id` INT NULL,
`ProductType_id` INT NOT NULL,
PRIMARY KEY (`id`),
INDEX `fk_Product_Location_idx` (`Location_id` ASC),
INDEX `fk_Product_ProductType1_idx` (`ProductType_id` ASC),
CONSTRAINT `fk_Product_Location`
FOREIGN KEY (`Location_id`)
REFERENCES `test`.`Location` (`id`)
ON DELETE NO ACTION
ON UPDATE NO ACTION,
CONSTRAINT `fk_Product_ProductType1`
FOREIGN KEY (`ProductType_id`)
REFERENCES `test`.`ProductType` (`id`)
ON DELETE NO ACTION
ON UPDATE NO ACTION)
ENGINE = InnoDB;
-- -----------------------------------------------------
-- Table `test`.`ProductType_has_Location`
-- -----------------------------------------------------
CREATE TABLE IF NOT EXISTS `test`.`ProductType_has_Location` (
`ProductType_id` INT NOT NULL,
`Location_id` INT NOT NULL,
PRIMARY KEY (`ProductType_id`, `Location_id`),
INDEX `fk_ProductType_has_Location_Location1_idx` (`Location_id` ASC),
INDEX `fk_ProductType_has_Location_ProductType1_idx` (`ProductType_id` ASC),
CONSTRAINT `fk_ProductType_has_Location_ProductType1`
FOREIGN KEY (`ProductType_id`)
REFERENCES `test`.`ProductType` (`id`)
ON DELETE NO ACTION
ON UPDATE NO ACTION,
CONSTRAINT `fk_ProductType_has_Location_Location1`
FOREIGN KEY (`Location_id`)
REFERENCES `test`.`Location` (`id`)
ON DELETE NO ACTION
ON UPDATE NO ACTION)
ENGINE = InnoDB;
INSERT INTO `test`.`Location`
(`name`)
VALUES
('fridge'),('shelf'),('cupboard');
INSERT INTO `test`.`ProductType`
(`name`)
VALUES
('food'),('drink'),('cosmetics');
INSERT INTO `test`.`ProductType_has_Location`
(`ProductType_id`,`Location_id`)
VALUES
(1,1),(2,1),(2,2),(3,3);
INSERT INTO `test`.`Product`
(`name`,`ProductType_id`,`Location_id`)
VALUES
('coke',2,NULL);

Answer 1

Another constraint in Product:
CONSTRAINT `fk_Product_Location_XRef`
FOREIGN KEY (`ProductType_id`,`Location_id`)
REFERENCES `test`.`ProductType_has_Location` (`ProductType_id`,`Location_id`)
ON DELETE NO ACTION
ON UPDATE NO ACTION
This then checks that the Type and Location agree with what's in the ProductType_has_Location table.